@article{bociu_muha_webster_2023, title={Mathematical effects of linear visco-elasticity in quasi-static Biot models ✩}, volume={527}, ISSN={["1096-0813"]}, DOI={10.1016/j.jmaa.2023.127462}, abstractNote={We investigate and clarify the mathematical properties of linear poro-elastic systems in the presence of classical (linear, Kelvin-Voigt) visco-elasticity. In particular, we quantify the time-regularizing and dissipative effects of visco-elasticity in the context of the quasi-static Biot equations. The full, coupled pressure-displacement presentation of the system is utilized, as well as the framework of implicit, degenerate evolution equations, to demonstrate such effects and characterize linear poro-visco-elastic systems. We consider a simple presentation of the dynamics (with convenient boundary conditions, etc.) for clarity in exposition across several relevant parameter ranges. Clear well-posedness results are provided, with associated a priori estimates on the solutions. In addition, precise statements of admissible initial conditions in each scenario are given.}, number={2}, journal={JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS}, author={Bociu, Lorena and Muha, Boris and Webster, Justin T.}, year={2023}, month={Nov} }
 @article{bociu_guidoboni_sacco_prada_2022, title={Numerical simulation and analysis of multiscale interface coupling between a poroelastic medium and a lumped hydraulic circuit: Comparison between functional iteration and operator splitting methods}, volume={466}, ISSN={["1090-2716"]}, url={https://doi.org/10.1016/j.jcp.2022.111379}, DOI={10.1016/j.jcp.2022.111379}, abstractNote={We consider a multiscale problem modeling the flow of a fluid through a deformable porous medium, described by a system of partial differential equations (PDEs), connected with a lumped hydraulic circuit, described by a system of ordinary differential equations (ODEs). This PDE/ODE coupled problem includes interface conditions enforcing the continuity of mass and the balance of stresses across models at different scales. In the present article, we address questions related to the solution methods of the PDE/ODE coupled problem via staggered algorithms, focusing on a detailed comparison between functional iterations and an energy-based operator splitting method and how they handle the interface conditions. We provide sufficient conditions for the convergence of functional iterations and prove that the energy-based operator splitting method is unconditionally stable with respect to the size of the time discretization step.}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Bociu, Lorena and Guidoboni, Giovanna and Sacco, Riccardo and Prada, Daniele}, year={2022}, month={Oct} }
 @article{bociu_muha_webster_2022, title={Weak solutions in nonlinear poroelasticity with incompressible constituents}, volume={67}, ISSN={["1878-5719"]}, DOI={10.1016/j.nonrwa.2022.103563}, abstractNote={We consider quasi-static nonlinear poroelastic systems with applications in biomechanics and, in particular, tissue perfusion.The nonlinear permeability is taken to be dependent on solid dilation, and physical types of boundary conditions (Dirichlet, Neumann, and mixed) for the fluid pressure are considered.The system under consideration represents a nonlinear, implicit, degenerate evolution problem, which falls outside of the well-known implicit semigroup monotone theory.Previous literature related to proving existence of weak solutions for these systems is based on constructing solutions as limits of approximations, and energy estimates are obtained only for the constructed solutions.In comparison, in this treatment we provide for the first time a direct, fixed point strategy for proving the existence of weak solutions, which is made possible by a novel result on the uniqueness of weak solutions of the associated linear system (where the permeability is given as a function of space and time).The uniqueness proof for the associated linear problem is based on novel energy estimates for arbitrary weak solutions, rather than just for constructed solutions.The results of this work provide a foundation for addressing strong solutions, as well as uniqueness of weak solutions for nonlinear poroelastic systems.}, journal={NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS}, author={Bociu, Lorena and Muha, Boris and Webster, Justin T.}, year={2022}, month={Oct} }
 @article{bociu_canic_muha_webster_2021, title={MULTILAYERED POROELASTICITY INTERACTING WITH STOKES FLOW}, volume={53}, ISSN={["1095-7154"]}, url={https://epubs.siam.org/doi/abs/10.1137/20M1382520}, DOI={10.1137/20M1382520}, abstractNote={We consider the interaction between an incompressible, viscous fluid modeled by the dynamic Stokes equation and a multilayered poroelastic structure which consists of a thin, linear, poroelastic plate layer (in direct contact with the free Stokes flow) and a thick Biot layer.The fluid flow and the elastodynamics of the multilayered poroelastic structure are fully coupled across a fixed interface through physical coupling conditions (including the Beavers-Joseph-Saffman condition), which present mathematical challenges related to the regularity of associated velocity traces.We prove the existence of weak solutions to this fluid-structure interaction problem with either (i) a linear, dynamic Biot model or (ii) a nonlinear quasi-static Biot component, where the permeability is a nonlinear function of the fluid content (as motivated by biological applications).The proof is based on constructing approximate solutions through Rothe's method and using energy methods and a version of the Aubin-Lions compactness lemma (in the nonlinear case) to recover the weak solution as the limit of approximate subsequences.We also provide uniqueness criteria and show that constructed weak solutions are indeed strong solutions to the coupled problem if one assumes additional regularity.}, number={6}, journal={SIAM JOURNAL ON MATHEMATICAL ANALYSIS}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Bociu, Lorena and Canic, Suncica and Muha, Boris and Webster, Justin T.}, year={2021}, pages={6243–6279} }
 @article{bociu_webster_2021, title={Nonlinear quasi-static poroelasticity & nbsp;}, volume={296}, ISSN={["1090-2732"]}, DOI={10.1016/j.jde.2021.05.060}, abstractNote={We analyze a quasi-static Biot system of poroelasticity for both compressible and incompressible constituents. The main feature of this model is a nonlinear coupling of pressure and dilation through the system's permeability tensor. Such a model has been analyzed previously from the point of view of constructing weak solutions through a fully discretized approach. In this treatment, we consider simplified Dirichlet type boundary conditions in both the elastic displacement and pressure variables and give a full treatment of weak solutions. Our construction of weak solutions for the nonlinear problem is based on a priori estimates, a requisite feature in addressing the nonlinearity. We utilize a spatial semi-discretization and employ a multi-valued fixed point argument for a clear construction of weak solutions. We also provide regularity criteria for uniqueness of solutions.}, journal={JOURNAL OF DIFFERENTIAL EQUATIONS}, author={Bociu, Lorena and Webster, Justin T.}, year={2021}, month={Sep}, pages={242–278} }
 @article{bociu_strikwerda_2021, title={Optimal control in poroelasticity}, volume={11}, ISSN={["1563-504X"]}, DOI={10.1080/00036811.2021.2008372}, abstractNote={In this paper we address optimal control problems subject to fluid flows through deformable, porous media. In particular, we focus on linear quadratic elliptic-parabolic control problems, with both distributed and boundary controls, and prove existence and uniqueness of optimal control. Furthermore, we derive the first order necessary optimality conditions. These problems have important biological and biomechanical applications. For example, optimizing the pressure of the flow, and investigating the influence and control of pertinent biological parameters are relevant in the case of the lamina cribrosa – a porous tissue at the base of the optic nerve head inside the eye – which is modeled by poroelasticity – where these factors are believed to be related to the development of ocular neurodegenerative diseases such as glaucoma. Moreover, the study and results will be applicable to other situations such as the poroelastic modeling of cartilages, bones, and engineered tissues.}, journal={APPLICABLE ANALYSIS}, author={Bociu, Lorena and Strikwerda, Sarah}, year={2021}, month={Nov} }
 @article{bociu_castle_lasiecka_tuffaha_2020, title={Minimizing drag in a moving boundary fluid-elasticity interaction}, volume={197}, ISSN={["1873-5215"]}, DOI={10.1016/j.na.2020.111837}, abstractNote={Our goal is to minimize the fluid vorticity in the case of an elastic body moving and deforming inside the fluid, using a distributed control. This translates into analyzing an optimal control problem subject to a moving boundary fluid–structure interaction (FSI). The FSI is described by the coupling of Navier–Stokes and wave equations. The control is inherently a nonlinear control, acting as feedback on the moving frame. Its action depends on the flow map of the domain, which is itself defined through the dynamics of the problem. A key ingredient in the optimal control problem is represented by the long time behavior of the forced dynamics, which was an open problem in the field. Our main results include existence of solutions for all times with small distributed sources and small initial data, as well as existence of optimal control for the problem of minimization of drag in the fluid.}, journal={NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS}, author={Bociu, L. and Castle, L. and Lasiecka, I and Tuffaha, A.}, year={2020}, month={Aug} }
 @article{banks_bekele-maxwell_bociu_noorman_guidiboni_2019, title={LOCAL SENSITIVITY VIA THE COMPLEX-STEP DERIVATIVE APPROXIMATION FOR 1D PORO-ELASTIC AND PORO-VISCO-ELASTIC MODELS}, volume={9}, ISSN={["2156-8499"]}, DOI={10.3934/mcrf.2019044}, abstractNote={Poro-elastic systems have been used extensively in modeling fluid flow in porous media in petroleum and earthquake engineering. Nowadays, they are frequently used to model fluid flow through biological tissues, cartilages, and bones. In these biological applications, the fluid-solid mixture problems, which may also incorporate structural viscosity, are considered on bounded domains with appropriate non-homogeneous boundary conditions. The recent work in [ 12 ] provided a theoretical and numerical analysis of nonlinear poro-elastic and poro-viscoelastic models on bounded domains with mixed boundary conditions, focusing on the role of visco-elasticity in the material. Their results show that higher time regularity of the sources is needed to guarantee bounded solution when visco-elasticity is not present. Inspired by their results, we have recently performed local sensitivity analysis on the solutions of these fluid-solid mixture problems with respect to the boundary source of traction associated with the elastic structure [ 3 ]. Our results show that the solution is more sensitive to boundary datum in the purely elastic case than when visco-elasticity is present in the solid matrix. In this article, we further extend this work in order to include local sensitivities of the solution of the coupled system to the boundary conditions imposed on the Darcy velocity. Sensitivity analysis is the first step in identifying important parameters to control or use as control terms in these poro-elastic and poro-visco-elastic models, which is our ultimate goal.}, number={4}, journal={MATHEMATICAL CONTROL AND RELATED FIELDS}, author={Banks, H. Thomas and Bekele-Maxwell, Kidist and Bociu, Lorena and Noorman, Marcelle and Guidiboni, Giovanna}, year={2019}, month={Dec}, pages={623–642} }
 @article{bociu_guidoboni_sacco_verri_2019, title={On the role of compressibility in poroviscoelastic models}, volume={16}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2019308}, abstractNote={In this article we conduct an analytical study of a poroviscoelastic mixture model stemming from the classical Biot's consolidation model for poroelastic media, comprising a fluid component and a solid component, coupled with a viscoelastic stress-strain relationship for the total stress tensor. The poroviscoelastic mixture is studied in the one-dimensional case, corresponding to the experimental conditions of confined compression. Upon assuming (i) negligible inertial effects in the balance of linear momentum for the mixture, (ii) a Kelvin-Voigt model for the effective stress tensor and (iii) a constant hydraulic permeability, we obtain an initial value/boundary value problem of pseudo-parabolic type for the spatial displacement of the solid component of the mixture. The dimensionless form of the differential equation is characterized by the presence of two positive parameters γ and η, representing the contributions of compressibility and structural viscoelasticity, respectively. Explicit solutions are obtained for different functional forms characterizing the boundary traction. The main result of our analysis is that the compressibility of the components of a poroviscoelastic mixture does not give rise to unbounded responses to non-smooth traction data. Interestingly, compressibility allows the system to store potential energy as its components are elastically compressed, thereby providing an additional mechanism that limits the maximum of the discharge velocity when the imposed boundary traction is irregular in time.}, number={5}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Bociu, Lorena and Guidoboni, Giovanna and Sacco, Riccardo and Verri, Maurizio}, year={2019}, pages={6167–6208} }
 @article{poro-visco-elastic models in biomechanics: sensitivity analysis_2019, DOI={10.12732/caa.v23i1.5}, journal={Communications in Applied Analysis}, year={2019} }
 @article{bociu_derochers_toundykov_2018, title={FEEDBACK STABILIZATION OF A LINEAR HYDRO-ELASTIC SYSTEM}, volume={23}, ISSN={["1553-524X"]}, DOI={10.3934/dcdsb.2018144}, abstractNote={It is known that the linear Stokes-Lame system can be stabilized by a boundary feedback in the form of a dissipative velocity matching on the common interface [ 5 ]. Here we consider feedback stabilization for a generalized linear fluid-elasticity interaction, where the matching conditions on the interface incorporate the curvature of the common boundary and thus take into account the geometry of the problem. Such a coupled system is semigroup well-posed on the natural finite energy space [ 13 ], however, the system is not dissipative to begin with, which represents a key departure from the feedback control analysis in [ 5 ]. We prove that a damped version of the general linear hydro-elasticity model is exponentially stable. First, such a result is given for boundary dissipation of the form used in [ 5 ]. This proof resolves a more complex version, compared to the classical case, of the weighted energy methods, and addresses the lack of over-determination in the associated unique continuation result. The second theorem demonstrates how assumptions can be relaxed if a viscous damping is added in the interior of the solid.}, number={3}, journal={DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B}, author={Bociu, Lorena and Derochers, Steven and Toundykov, Daniel}, year={2018}, month={May}, pages={1107–1132} }
 @article{verri_guidoboni_bociu_sacco_2018, title={THE ROLE OF STRUCTURAL VISCOELASTICITY IN DEFORMABLE POROUS MEDIA WITH INCOMPRESSIBLE CONSTITUENTS: APPLICATIONS IN BIOMECHANICS}, volume={15}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2018042}, abstractNote={The main goal of this work is to clarify and quantify, by means of mathematical analysis, the role of structural viscoelasticity in the biomechanical response of deformable porous media with incompressible constituents to sudden changes in external applied loads. Models of deformable porous media with incompressible constituents are often utilized to describe the behavior of biological tissues, such as cartilages, bones and engineered tissue scaffolds, where viscoelastic properties may change with age, disease or by design. Here, for the first time, we show that the fluid velocity within the medium could increase tremendously, even up to infinity, should the external applied load experience sudden changes in time and the structural viscoelasticity be too small. In particular, we consider a one-dimensional poro-visco-elastic model for which we derive explicit solutions in the cases where the external applied load is characterized by a step pulse or a trapezoidal pulse in time. By means of dimensional analysis, we identify some dimensionless parameters that can aid the design of structural properties and/or experimental conditions as to ensure that the fluid velocity within the medium remains bounded below a certain given threshold, thereby preventing potential tissue damage. The application to confined compression tests for biological tissues is discussed in detail. Interestingly, the loss of viscoelastic tissue properties has been associated with various disease conditions, such as atherosclerosis, Alzheimer's disease and glaucoma. Thus, the findings of this work may be relevant to many applications in biology and medicine.}, number={4}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Verri, Maurizio and Guidoboni, Giovanna and Bociu, Lorena and Sacco, Riccardo}, year={2018}, month={Aug}, pages={933–959} }
 @article{banks_bekele-maxwell_bociu_noorman_guidoboni_2017, title={SENSITIVITY ANALYSIS IN PORO-ELASTIC AND PORO-VISCO-ELASTIC MODELS WITH RESPECT TO BOUNDARY DATA}, volume={75}, ISSN={["1552-4485"]}, DOI={10.1090/qam/1475}, abstractNote={In this article we consider poro-elastic and poro-visco-elastic models inspired by problems in medicine and biology, and we perform sensitivity analysis on the solutions of these fluid-solid mixture problems with respect to the imposed boundary data, which are the main drivers of the system. Moreover, we compare the results obtained in the elastic case vs. visco-elastic case, as it is known that structural viscosity of biological tissues decreases with age and disease. Sensitivity analysis is the first step towards optimization and control problems associated with these models, which is our ultimate goal.}, number={4}, journal={QUARTERLY OF APPLIED MATHEMATICS}, author={Banks, H. T. and Bekele-Maxwell, K. and Bociu, L. and Noorman, M. and Guidoboni, G.}, year={2017}, month={Dec}, pages={697–735} }
 @article{banks_bekele-maxwell_bociu_wang_2017, title={SENSITIVITY VIA THE COMPLEX-STEP METHOD FOR DELAY DIFFERENTIAL EQUATIONS WITH NON-SMOOTH INITIAL DATA}, volume={75}, ISSN={["1552-4485"]}, DOI={10.1090/qam/1458}, abstractNote={In this report, we use the complex-step derivative approximation technique to compute sensitivities for delay differential equations (DDEs) with non-smooth (discontinuous and even distributional) history functions. We compare the results with exact derivatives and with those computed using the classical sensitivity equations whenever possible. Our results demonstrate that the implementation of the complex-step method using the method of steps and the Matlab solver dde23 provides a very good approximation of sensitivities as long as discontinuities in the initial data do not cause loss of smoothness in the solution: that is, even when the underlying smoothness with respect to the initial data for the Cauchy-Riemann derivation of the method does not hold. We conclude with remarks on our findings regarding the complex-step method for computing sensitivities for simpler ordinary differential equation systems in the event of lack of smoothness with respect to parameters.}, number={2}, journal={QUARTERLY OF APPLIED MATHEMATICS}, author={Banks, H. T. and Bekele-Maxwell, Kidist and Bociu, Lorena and Wang, Chuyue}, year={2017}, month={Jun}, pages={231–248} }
 @article{bociu_guidoboni_sacco_webster_2016, title={Analysis of Nonlinear Poro-Elastic and Poro-Visco-Elastic Models}, volume={222}, ISSN={0003-9527 1432-0673}, url={http://dx.doi.org/10.1007/s00205-016-1024-9}, DOI={10.1007/s00205-016-1024-9}, abstractNote={We consider the initial and boundary value problem for a system of partial differential equations describing the motion of a fluid–solid mixture under the assumption of full saturation. The ability of the fluid phase to flow within the solid skeleton is described by the permeability tensor, which is assumed here to be a multiple of the identity and to depend nonlinearly on the volumetric solid strain. In particular, we study the problem of the existence of weak solutions in bounded domains, accounting for non-zero volumetric and boundary forcing terms. We investigate the influence of viscoelasticity on the solution functional setting and on the regularity requirements for the forcing terms. The theoretical analysis shows that different time regularity requirements are needed for the volumetric source of linear momentum and the boundary source of traction depending on whether or not viscoelasticity is present. The theoretical results are further investigated via numerical simulations based on a novel dual mixed hybridized finite element discretization. When the data are sufficiently regular, the simulations show that the solutions satisfy the energy estimates predicted by the theoretical analysis. Interestingly, the simulations also show that, in the purely elastic case, the Darcy velocity and the related fluid energy might become unbounded if indeed the data do not enjoy the time regularity required by the theory.}, number={3}, journal={Archive for Rational Mechanics and Analysis}, publisher={Springer Nature}, author={Bociu, Lorena and Guidoboni, Giovanna and Sacco, Riccardo and Webster, Justin T.}, year={2016}, month={Jul}, pages={1445–1519} }
 @article{free boundary fluid-elasticity interactions: adjoint sensitivity analysis_2016, journal={New Trends in Differential Equations, Control Theory and Optimization}, year={2016} }
 @inproceedings{bociu_martin_2016, title={Free boundary fluid-elasticity interactions: Adjoint sensitivity analysis}, ISBN={9789813142855 9789813142862}, url={http://dx.doi.org/10.1142/9789813142862_0002}, DOI={10.1142/9789813142862_0002}, booktitle={New Trends in Differential Equations, Control Theory and Optimization}, publisher={WORLD SCIENTIFIC}, author={Bociu, Lorena and Martin, Kristina}, year={2016}, month={Jun} }
 @article{bociu_zolésio_2016, title={Hyperbolic Equations with Mixed Boundary Conditions: Shape Differentiability Analysis}, volume={76}, ISSN={0095-4616 1432-0606}, url={http://dx.doi.org/10.1007/s00245-016-9354-4}, DOI={10.1007/s00245-016-9354-4}, number={2}, journal={Applied Mathematics & Optimization}, publisher={Springer Science and Business Media LLC}, author={Bociu, Lorena and Zolésio, Jean-Paul}, year={2016}, month={Apr}, pages={375–398} }
 @article{bociu_derochers_toundykov_2016, title={LINEARIZED HYDRO-ELASTICITY: A NUMERICAL STUDY}, volume={5}, ISSN={["2163-2480"]}, DOI={10.3934/eect.2016018}, abstractNote={In view of control and stability theory, a recently obtained linearization around a steady state of a fluid-structure interaction is considered. The linearization was performed with respect to an external forcing term and was derived in an earlier paper via shape optimization techniques. In contrast to other approaches, like transporting to a fixed reference configuration, or using transpiration techniques, the shape optimization route is most suited to incorporating the geometry of the problem into the analysis. This refined description brings up new terms---missing in the classical coupling of linear Stokes flow and linear elasticity---in the matching of the normal stresses and the velocities on the interface. 
 Later, it was demonstrated that this linear PDE system generates a $C_0$ semigroup, however, unlike in the standard Stokes-elasticity coupling, the wellposedness result depended on the fluid's viscosity and the new boundary terms which, among other things, involve the curvature of the interface. 
Here, we implement a finite element scheme for approximating solutions of this fluid-elasticity dynamics and numerically investigate the dependence of the discretized model on the ``new" terms present therein, in contrast with the classical Stokes-linear elasticity system.}, number={4}, journal={EVOLUTION EQUATIONS AND CONTROL THEORY}, author={Bociu, Lorena and Derochers, Steven and Toundykov, Daniel}, year={2016}, month={Dec}, pages={533–559} }
 @article{bociu_zolesio_2015, title={A pseudo-extractor approach to hidden boundary regularity for the wave equation with mixed boundary conditions}, volume={259}, ISSN={["1090-2732"]}, DOI={10.1016/j.jde.2015.07.006}, abstractNote={In this paper we introduce a new approach to “hidden” boundary regularity for the linear wave equation with mixed Dirichlet–Neumann boundary conditions, where the Neumann data is non-smooth. First, we obtain existence and uniqueness of solution by Galerkin estimates. Then we use a new, pseudo-extractor technique (based on the Fourier transform and shape and tangential calculus) in order to provide sharp regularity for the solution at the boundary.}, number={11}, journal={JOURNAL OF DIFFERENTIAL EQUATIONS}, author={Bociu, Lorena and Zolesio, Jean-Paul}, year={2015}, month={Dec}, pages={5688–5708} }
 @inproceedings{toundykov_martin_castle_bociu_2015, title={Optimal control in a free boundary fluid-elasticity interaction}, ISBN={1601330189}, url={http://dx.doi.org/10.3934/proc.2015.0122}, DOI={10.3934/proc.2015.0122}, abstractNote={We establish existence of an optimal control for the problem of minimizing flow turbulence in the case of a nonlinear fluid-structure interaction model in the framework of the known local well-posedness theory. If the initial configuration is regular, in an appropriate sense, then a class of sufficiently smooth control inputs contains an element that minimizes, within the control class, the vorticity of the fluid flow around a moving and deforming elastic solid.}, booktitle={Dynamical Systems and Differential Equations, AIMS Proceedings 2015 Proceedings of the 10th AIMS International Conference (Madrid, Spain)}, publisher={American Institute of Mathematical Sciences}, author={Toundykov, Daniel and Martin, Kristina and Castle, Lucas and Bociu, Lorena}, year={2015}, month={Nov} }
 @article{bociu_banks_bekele-maxwell_noorman_tillman_2015, title={The complex-step method for sensitivity analysis of non-smooth problems arising in biology}, volume={3}, ISSN={2306-6172}, number={3}, journal={Eurasian Journal of Mathematical and Computer Applications}, author={Bociu, Lorena and Banks, H.T. and Bekele-Maxwell, K. and Noorman, M. and Tillman, K.}, year={2015}, pages={16–68} }
 @article{bociu_toundykov_zolesio_2015, title={WELL-POSEDNESS ANALYSIS FOR A LINEARIZATION OF A FLUID-ELASTICITY INTERACTION}, volume={47}, ISSN={["1095-7154"]}, DOI={10.1137/140970689}, abstractNote={We study the well-posedness of a total linearization, with respect to a perturbation of the external forcing, of a free-boundary nonlinear elasticity--incompressible fluid interaction. The total linearization for the coupling modeled by the Navier--Stokes equations and the nonlinear equations of elastodynamics was obtained recently in [L. Bociu and J.-P. Zolesio, Evol. Equ. Control Theory, 2 (2013), pp. 55--79]. The equations and the free boundary were linearized together, and the result turned out to be quite different from the usual coupling of classical linear models. New additional terms are present on the common interface, some of them involving boundary curvatures and boundary acceleration. These terms play an important role in the final linearized system and cannot be neglected; their presence also introduces new challenges in the well-posedness analysis, which proceeds to establish that the evolution operator associated to the linearized system can be represented as a bounded perturbation of a max...}, number={3}, journal={SIAM JOURNAL ON MATHEMATICAL ANALYSIS}, author={Bociu, Lorena and Toundykov, Daniel and Zolesio, Jean-Paul}, year={2015}, pages={1958–2000} }
 @article{bociu_toundykov_2014, title={Corrigendum to “Attractors for non-dissipative irrotational von Karman plates with boundary damping” [J. Differential Equations 253 (12) (2012) 3568–3609]}, volume={256}, ISSN={0022-0396}, url={http://dx.doi.org/10.1016/J.JDE.2013.10.007}, DOI={10.1016/J.JDE.2013.10.007}, number={2}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Bociu, Lorena and Toundykov, Daniel}, year={2014}, month={Jan}, pages={893} }
 @article{bociu_radu_toundykov_2014, title={ERRATA: REGULAR SOLUTIONS OF WAVE EQUATIONS WITH SUPER-CRITICAL SOURCES AND EXPONENTIAL-TO-LOGARITHMIC DAMPING}, volume={3}, ISSN={["2163-2480"]}, DOI={10.3934/eect.2014.3.349}, abstractNote={This note is an errata for the paper [2] which discusses regular solutions to wave equations with super-critical source terms. The purpose of this note is to address the gap in the proof of uniqueness of such solutions.}, number={2}, journal={EVOLUTION EQUATIONS AND CONTROL THEORY}, author={Bociu, Lorena and Radu, Petronela and Toundykov, Daniel}, year={2014}, month={Jun}, pages={349–354} }
 @article{bociu_zolésio_2013, title={Sensitivity analysis for a free boundary fluid-elasticity interaction}, volume={2}, ISSN={2163-2480}, url={http://dx.doi.org/10.3934/eect.2013.2.55}, DOI={10.3934/eect.2013.2.55}, abstractNote={In this paper a total linearization is derived for the free boundary nonlinear elasticity - incompressible fluid interaction. The equations and the free boundary are linearized together and the new linearization turns out to be different from the usual 
coupling of classical linear models. New extra terms are present on the common interface, some of them involving the boundary curvatures. These terms play an important role 
in the final linearized system and can not be neglected.}, number={1}, journal={Evolution Equations and Control Theory}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Bociu, Lorena and Zolésio, Jean-Paul}, year={2013}, month={Jan}, pages={55–79} }
 @inbook{zolésio_bociu_2013, title={Strong Shape Derivative for the Wave Equation with Neumann Boundary Condition}, ISBN={9783642360619 9783642360626}, ISSN={1868-4238 1861-2288}, url={http://dx.doi.org/10.1007/978-3-642-36062-6_45}, DOI={10.1007/978-3-642-36062-6_45}, abstractNote={The paper provides shape derivative analysis for the wave equation with mixed boundary conditions on a moving domain Ω s in the case of non smooth neumann boundary datum. The key ideas in the paper are (i) bypassing the classical sensitivity analysis of the state by using parameter differentiability of a functional expressed in the form of Min-Max of a convex-concave Lagrangian with saddle point, and (ii) using a new regularity result on the solution of the wave problem (where the Dirichlet condition on the fixed part of the boundary is essential) to analyze the strong derivative.}, booktitle={IFIP Advances in Information and Communication Technology}, publisher={Springer Berlin Heidelberg}, author={Zolésio, Jean-Paul and Bociu, Lorena}, year={2013}, pages={445–460} }
 @article{strong shape derivative for the wave equation with neumann boundary condition_2013, journal={D. Homberg and F. Troltzsch (Eds.): CSMO 2011, IFIP AICT 391, International Federation for Information Processing}, year={2013} }
 @article{bociu_toundykov_2013, title={Wave equations with nonlinear sources and damping: weak vs. regular solutions}, volume={2}, number={2}, journal={Palestine Journal of Mathematics}, author={Bociu, Lorena and Toundykov, D.}, year={2013}, pages={175–186} }
 @article{bociu_toundykov_2012, title={Attractors for non-dissipative irrotational von Karman plates with boundary damping}, volume={253}, ISSN={["1090-2732"]}, DOI={10.1016/j.jde.2012.08.004}, abstractNote={Long-time behavior of solutions to a von Karman plate equation is considered. The system has an unrestricted first-order perturbation and a nonlinear damping acting through free boundary conditions only. This model differs from those previously considered (e.g. in the extensive treatise (Chueshov and Lasiecka, 2010 [11])) because the semi-flow may be of a non-gradient type: the unique continuation property is not known to hold, and there is no strict Lyapunov function on the natural finite-energy space. Consequently, global bounds on the energy, let alone the existence of an absorbing ball, cannot be a priori inferred. Moreover, the free boundary conditions are not recognized by weak solutions and some helpful estimates available for clamped, hinged or simply-supported plates cannot be invoked. It is shown that this non-monotone flow can converge to a global compact attractor with the help of viscous boundary damping and appropriately structured restoring forces acting only on the boundary or its collar.}, number={12}, journal={JOURNAL OF DIFFERENTIAL EQUATIONS}, author={Bociu, Lorena and Toundykov, Daniel}, year={2012}, month={Dec}, pages={3568–3609} }
 @article{bociu_rammaha_toundykov_2012, title={Wave equations with super-critical interior and boundary nonlinearities}, volume={82}, ISSN={0378-4754}, url={http://dx.doi.org/10.1016/j.matcom.2011.04.006}, DOI={10.1016/j.matcom.2011.04.006}, abstractNote={This article presents a unified overview of the latest, to date, results on boundary value problems for wave equations with super-critical nonlinear sources on both the interior and the boundary of a bounded domain Ω∈Rn. The presented theorems include Hadamard local wellposedness, global existence, blow-up and non-existence theorems, as well as estimates on the uniform energy dissipation rates for the appropriate classes of solutions.}, number={6}, journal={Mathematics and Computers in Simulation}, publisher={Elsevier BV}, author={Bociu, Lorena and Rammaha, Mohammad and Toundykov, Daniel}, year={2012}, month={Feb}, pages={1017–1029} }
 @inbook{bociu_zolésio_2011, title={Existence for the linearization of a steady state fluid/nonlinear elasticity interaction}, ISBN={1601330111}, url={http://dx.doi.org/10.3934/proc.2011.2011.184}, DOI={10.3934/proc.2011.2011.184}, abstractNote={A linearized steady state three-dimensional fluid-structure interaction is considered and its solvability is studied. The linearization (obtained in a previous work by these authors) that we deal with has new features, including the presence of the curvature terms on the common interface. These new extra terms, coming from the geometrical aspect of the problem, are critical for a correct physical interpretation of the fluid/structure coupling. We prove that the linearization has unique solution.}, booktitle={Discrete and Continuous Dynamical Systems}, publisher={AIMS Press}, author={Bociu, Lorena and Zolésio, Jean-Paul}, year={2011}, pages={184–197} }
 @inbook{bociu_zolésio_2011, title={Linearization of a Coupled System of Nonlinear Elasticity and Viscous Fluid}, ISBN={9783034800686 9783034800693}, url={http://dx.doi.org/10.1007/978-3-0348-0069-3_6}, DOI={10.1007/978-3-0348-0069-3_6}, booktitle={Modern Aspects of the Theory of Partial Differential Equations}, publisher={Springer Basel}, author={Bociu, Lorena and Zolésio, Jean-Paul}, year={2011}, pages={93–120} }
 @article{bociu_rammaha_toundykov_2011, title={On a wave equation with supercritical interior and boundary sources and damping terms}, volume={284}, ISSN={0025-584X}, url={http://dx.doi.org/10.1002/mana.200910182}, DOI={10.1002/mana.200910182}, abstractNote={This article addresses nonlinear wave equations with supercritical interior and boundary sources, and subject to interior and boundary damping. The presence of a nonlinear boundary source alone is known to pose a significant difficulty since the linear Neumann problem for the wave equation is not, in general, well‐posed in the finite‐energy space H1(Ω) × L2(∂Ω) with boundary data in L2 due to the failure of the uniform Lopatinskii condition. Further challenges stem from the fact that both sources are non‐dissipative and are not locally Lipschitz operators from H1(Ω) into L2(Ω), or L2(∂Ω). With some restrictions on the parameters in the model and with careful analysis involving the Nehari Manifold, we obtain global existence of a unique weak solution, and establish exponential and algebraic uniform decay rates of the finite energy (depending on the behavior of the dissipation terms). Moreover, we prove a blow up result for weak solutions with nonnegative initial energy.}, number={16}, journal={Mathematische Nachrichten}, publisher={Wiley}, author={Bociu, Lorena and Rammaha, Mohammad and Toundykov, Daniel}, year={2011}, month={Aug}, pages={2032–2064} }
 @article{bociu_lasiecka_2010, title={Local Hadamard well-posedness for nonlinear wave equations with supercritical sources and damping}, volume={249}, ISSN={0022-0396}, url={http://dx.doi.org/10.1016/j.jde.2010.03.009}, DOI={10.1016/j.jde.2010.03.009}, abstractNote={We consider the wave equation with supercritical interior and boundary sources and damping terms. The main result of the paper is local Hadamard well-posedness of finite energy (weak) solutions. The results obtained: (1) extend the existence results previously obtained in the literature (by allowing more singular sources); (2) show that the corresponding solutions satisfy Hadamard well-posedness conditions during the time of existence. This result provides a positive answer to an open question in the area and it allows for the construction of a strongly continuous semigroup representing the dynamics governed by the wave equation with supercritical sources and damping.}, number={3}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Bociu, Lorena and Lasiecka, Irena}, year={2010}, month={Aug}, pages={654–683} }
 @article{existence and uniqueness of weak solutions to the cauchy problem of a semilinear wave equation with supercritical interior source and damping_2009, journal={Dynamical Systems and Differential Equations - S}, year={2009} }
 @inbook{bociu_radu_2009, title={Existence of weak solutions to the Cauchy problem of a semilinear wave equation with supercritical interior source and damping}, ISBN={1601330073}, url={http://dx.doi.org/10.3934/proc.2009.2009.60}, DOI={10.3934/proc.2009.2009.60}, abstractNote={In this paper we show existence of finite energy solutions for the Cauchy problem associated with a semilinear wave equation with interior damping and supercritical source terms. The main contribution consists in dealing with super-supercritical source terms (terms of the order of $|u|^p$ with $p\geq 5$ in $n=3$ dimensions), an open and highly recognized problem in the literature on nonlinear wave equations.}, booktitle={Dynamical Systems and Differential Equations}, publisher={AIMS Press}, author={Bociu, Lorena and Radu, P.}, year={2009}, pages={60–71} }
 @article{bociu_2009, title={Local and global wellposedness of weak solutions for the wave equation with nonlinear boundary and interior sources of supercritical exponents and damping}, volume={71}, ISSN={0362-546X}, url={http://dx.doi.org/10.1016/j.na.2008.11.062}, DOI={10.1016/j.na.2008.11.062}, abstractNote={We consider the wave equation with interior and boundary nonlinear sources and damping and we are interested in local and global wellposedness of finite energy solutions. The main difficulty is represented by the fact that the Lopatinski condition fails to hold (unless the dim(Ω)=1), and thus the analysis of the boundary nonlinearities becomes a subtle issue.}, number={12}, journal={Nonlinear Analysis: Theory, Methods & Applications}, publisher={Elsevier BV}, author={Bociu, Lorena}, year={2009}, month={Dec}, pages={e560–e575} }
 @article{bociu_lasiecka_2008, title={Blow-up of weak solutions for the semilinear wave equations with nonlinear boundary and interior sources and damping}, volume={35}, ISSN={1233-7234 1730-6280}, url={http://dx.doi.org/10.4064/am35-3-3}, DOI={10.4064/am35-3-3}, abstractNote={We focus on the blow-up in finite time of weak solutions to the wave equation with interior and boundary nonlinear sources and dissipations. Our central interest is the relationship of the sources and damping terms to the behavior of solutions. We prove that under specific conditions relating the sources and the dissipations (namely p > m and k > m), weak solutions blow up in finite time.}, number={3}, journal={Applicationes Mathematicae}, publisher={Institute of Mathematics, Polish Academy of Sciences}, author={Bociu, Lorena and Lasiecka, Irena}, year={2008}, pages={281–304} }
 @phdthesis{existence, uniqueness, and blow-up of solutions to wave equations with supercritical boundary/interior sources and damping_2008, year={2008} }
 @article{lasiecka_bociu_2008, title={Uniqueness of weak solutions for the semilinear wave equations with supercritical boundary/interior sources and damping}, volume={22}, ISSN={1078-0947}, url={http://dx.doi.org/10.3934/dcds.2008.22.835}, DOI={10.3934/dcds.2008.22.835}, abstractNote={We consider finite energy solutions of a wave equation with 
supercritical nonlinear sources and nonlinear damping. A distinct 
feature of the model under consideration is the presence of 
nonlinear sources on the boundary driven by Neumann boundary 
conditions. Since Lopatinski condition fails to hold (unless the 
$\text{dim} (\Omega) = 1$), the analysis of the nonlinearities 
supported on the boundary, within the framework of weak solutions, 
is a rather subtle issue and involves the strong interaction between 
the source and the damping. Thus, it is not surprising that 
existence theory for this class of problems has been established 
only recently. However, the uniqueness of weak solutions was 
declared an open problem. The main result in this work is 
uniqueness of weak solutions. This result is proved for the 
same (even larger) class of data for which existence theory holds. 
In addition, we prove that weak solutions are continuously depending 
on initial data and that the flow corresponding to weak and global 
solutions 
 is a dynamical system on the finite 
energy space.}, number={4}, journal={Discrete and Continuous Dynamical Systems}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Lasiecka, Irena and Bociu, Lorena}, year={2008}, month={Sep}, pages={835–860} }
 @inproceedings{bociu_lasiecka_2006, title={Wellposedness and Blow-up of Solutions to Wave Equations with Supercritical Boundary Sources and Boundary Damping}, booktitle={Proceedings of the Conference on Differential and Difference Equations and Applications}, publisher={Hindawi Publishing Corporation}, author={Bociu, Lorena and Lasiecka, I.}, year={2006}, pages={635–643} }
 @article{wellposedness and blow-up of solutions to wave equations with supercritical boundary sources and boundary damping_2006, journal={Proceedings of the Conference on Differential and Difference Equations and Applications}, year={2006} }
 @article{multilayered poroelasticity interacting with stokes flow, journal={SIAM Journal on Mathematical Analysis} }