Michael Shearer

Traveling Wave Solutions of the Kawahara Equation Joining Distinct Periodic Waves

JOURNAL OF NONLINEAR SCIENCE, 33(5).

Well-posedness and ill-posedness of single-phase models for suspensions

JOURNAL OF FLUID MECHANICS, 954.

Dispersive Riemann problems for the Benjamin-Bona-Mahony equation

Congy, T., El, G. A., Hoefer, M. A., & Shearer, M. (2021, August 24). STUDIES IN APPLIED MATHEMATICS, Vol. 8.

Gradient-induced droplet motion over soft solids

IMA Journal of Applied Mathematics, 85(3), 495–512.

Constitutive relations for compressible granular flow in the inertial regime

JOURNAL OF FLUID MECHANICS, 874, 926–951.

Distinguishing deformation mechanisms in elastocapillary experiments

Soft Matter, 15(46), 9426–9436.

A SCALAR CONSERVATION LAW FOR PLUME MIGRATION IN CARBON SEQUESTRATION

SIAM JOURNAL ON APPLIED MATHEMATICS, 78(3), 1823–1841.

Nonlinear Schrödinger equations and the universal description of dispersive shock wave structure

Studies in Applied Mathematics, 142(3), 241–268.

Nonlocal rheology of dense granular flow in annular shear experiments

Soft Matter, 14(16), 3040–3048.

Deformation of an elastic substrate due to a resting sessile droplet

European Journal of Applied Mathematics, 29(2), 281–300.

Dispersive and Diffusive-Dispersive ShockWaves for Nonconvex Conservation Laws

SIAM REVIEW, 59(1), 3–61.

Stationary Expansion Shocks for a Regularized Boussinesq System

Studies in Applied Mathematics, 139(4), 1–22.

Well-posed continuum equations for granular flow with compressibility and μ ( I )-rheology

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473(2201), 20160846.

Wetting dynamics of a collapsing fluid hole

PHYSICAL REVIEW FLUIDS, 2(1).

Expansion shock waves in regularized shallow-water theory

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 472(2189), 20160141.

Partial differential equations: An introduction to theory and applications

Princeton: Princeton University Press.

Spatiotemporal measurement of surfactant distribution on gravity-capillary waves

JOURNAL OF FLUID MECHANICS, 777.

Surfactant spreading on a thin liquid film: reconciling models and experiments

Swanson, E. R., Strickland, S. L., Shearer, M., & Daniels, K. E. (2015, October). JOURNAL OF ENGINEERING MATHEMATICS, Vol. 94, pp. 63–79.

Traveling waves for conservation laws with cubic nonlinearity and BBM type dispersion

JOURNAL OF DIFFERENTIAL EQUATIONS, 259(7), 3216–3232.

Elastocapillary deformations on partially-wetting substrates: rival contact-line models

Soft Matter, 10(37), 7361.

Two Fluid Flow in a Capillary Tube

Smooth Periodic Solutions of a 2x2 System of Nonlinear Hyperbolic Conservation Laws

Applied Mathematics Research EXpress, 7.

Two Fluid Flow in Porous Media

Proceedings of HYP2012, 8, 212–232. American Institute of Mathematical Sciences.

Simulation of spreading surfactant on a thin liquid film

Applied Mathematics and Computation, 218(9), 5157–5167.

Stability of plane waves in two-phase porous media flow

APPLICABLE ANALYSIS, 91(2), 295–308.

THE BUCKLEY-LEVERETT EQUATION WITH DYNAMIC CAPILLARY PRESSURE

SIAM JOURNAL ON APPLIED MATHEMATICS, 71(4), 1088–1108.

Evolution of a Mixing Zone in Granular Avalanches

Applied Mathematics Research EXpress, 7.

FINITE TIME EMERGENCE OF A SHOCK WAVE FOR SCALAR CONSERVATION LAWS

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 7(1), 107–116.

Radial Spreading of a Surfactant on a Thin Liquid Film

Applied Mathematics Research EXpress, 9.

SHOCK FORMATION AND BREAKING IN GRANULAR AVALANCHES

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 27(2), 693–714.

Scalar Conservation Laws with Nonconstant Coefficients with Application to Particle Size Segregation in Granular Flow

Journal of Nonlinear Science, 20(6), 689–707.

Shear-driven size segregation of granular materials: Modeling and experiment

PHYSICAL REVIEW E, 81(5).

The Gray-Thornton Model of Granular Segregation

Presented at the IUTAM-ISIMM SYMPOSIUM ON MATHEMATICAL MODELING AND PHYSICAL INSTANCES OF GRANULAR FLOWS.

Periodic motion of a mass-spring system

IMA JOURNAL OF APPLIED MATHEMATICS, 74(6), 807–826.

Stability of traveling waves in thin liquid films driven by gravity and surfactant

Stable solutions of a scalar conservation law for particle-size segregation in dense granular avalanches

EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 19, 61–86.

Automated Review of Prerequisite Material for Intermediate-Level Undergraduate Mathematics

PRIMUS, 17(2), 167–180.

Boundary-value problems for hyperbolic equations related to steady granular flow

MATHEMATICS AND MECHANICS OF SOLIDS, 12(6), 665–699.

Gravity-driven thin liquid films with insoluble surfactant: smooth traveling waves

European Journal of Applied Mathematics, 18(6), 679–708.

Growing surfactant waves in thin liquid films driven by gravity

Applied Mathematics Research EXpress, 1.

The Motion of a Thin Liquid Film Driven by Surfactant and Gravity

SIAM Journal on Applied Mathematics, 66(5), 1588–1609.

Time-dependent solutions for particle-size segregation in shallow granular avalanches

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 462(2067), 947–972.

Kinetics and nucleation for driven thin film flow

Physica D: Nonlinear Phenomena, 209(1-4), 145–163.

Non-linear dynamics of thin films and fluid interfaces - Preface

Behringer, R. P., & Shearer, M. (2005, September 15). PHYSICA D-NONLINEAR PHENOMENA, Vol. 209, pp. VII-VIII.

Comparison of two dynamic contact line models for driven thin liquid films

European Journal of Applied Mathematics, 15(6), 625–642.

Non-classical Riemann solvers with nucleation

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 134(2004), 961–984.

Stability of shear bands in an elastoplastic model for granular flow: The role of discreteness

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 13(11), 1629–1671.

Thin film traveling waves and the Navier slip condition

SIAM Journal on Applied Mathematics, 63(2), 722–744.

Computer simulations of particle deposition in the lungs of chronic obstructive pulmonary disease patients

INHALATION TOXICOLOGY, 14(7), 705–720.

A discrete model for an ill-posed nonlinear parabolic PDE

PHYSICA D-NONLINEAR PHENOMENA, 160(3-4), 189–221.

A nonconvex scalar conservation law with trilinear flux

QUARTERLY OF APPLIED MATHEMATICS, 59(4), 615–635.

Stability of compressive and undercompressive thin film travelling waves

EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 12(2001 June), 253–291.

Existence of undercompressive traveling waves in thin film equations

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 32(1), 194–213.

Mathematical Model of Airflow in the Lungs of Children I: Effects of Tumor Sizes and Locations

Journal of Theoretical Medicine, 2(3), 199–213.

Mathematical Model of Airflow in the Lungs of Children II: Effects of Ventilatory Parameters

Journal of Theoretical Medicine, 3(1), 51–62.

Numerical determination of flow corrective inserts for granular materials in conical hoppers

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 35(5), 869–882.

Similarity solutions for granular flows in hoppers

Undercompressive shocks and Riemann problems for scalar conservation laws with non-convex fluxes

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 129(1999), 733–754.

Undercompressive shocks for a system of hyperbolic conservation laws with cubic nonlinearity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 229(1), 344–362.

Undercompressive shocks in thin film flows

PHYSICA D-NONLINEAR PHENOMENA, 134(4), 431–464.

Undercompressive waves in driven thin film flow: Theory, computation, and experiment

In V. Alexiades & G. Siopsis (Eds.), Trends in Mathematical Physics (Vol. 13, pp. 43–68).

A simple model for stress fluctuations in plasticity with application to granular materials

SIAM JOURNAL ON APPLIED MATHEMATICS, 58(6), 1791–1807.

An elastoplasticity model for antiplane shearing with a non-associative flow rule: Genuine nonlinearity of plastic waves

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 219(2), 344–363.

Discrete element investigation of stress fluctuation in granular flow at high strain rates

PHYSICAL REVIEW E, 57(2), 2053–2061.

Lithotripsy: The treatment of kidney stones with shock waves

SIAM REVIEW, 40(2), 356–371.

Formation of Shear Bands in Models of Granular Materials

In IUTAM Symposium on Mechanics of Granular and Porous Materials (pp. 343–352).

Models for stress fluctuations in plasticity

In R. P. Behringer & J. Jenkins (Eds.), Powders & grains 97 : proceedings of the third International Conference on Powders & Grains, Durham, North Carolina, 18-23 May 1997 (pp. 325–328). Rotterdam, Netherlands: Balkema.

Plane shear waves in a fully saturated granular medium with velocity and stress controlled boundary conditions

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 32(3), 489–503.

Stress fluctuations in granular materials

In C. S. Chang, A. Misra, R. Y. Liang, & M. Babic (Eds.), Mechanics of deformation and flow of particulate materials : proceedings of a symposium, Evanston, Illinois, June 29-July 2, 1997. New York: ASCE Publications.

The influence of material non-uniformity preceding shear-band formation in a model for granular flow

EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 8(1997 Oct.), 457–483.

Fully nonlinear hyperbolic systems related to hypoplasticity

In J. Glimm, M. J. Graham, J. W. Grove, & B. J. Plohr (Eds.), Proceedings of the Fifth International Conference on Hyperbolic problems: Theory, numerics, applications (pp. 440–446). River Edge, New Jersey: World Scientific.

Riemann Problems for 5×5 Systems of Fully Non-linear Equations Related to Hypoplasticity

Mathematical Methods in the Applied Sciences, 19(18), 1433–1444.

A class of fully nonlinear 2×2 systems of partial differential equations

Communications in Partial Differential Equations, 20(7-8), 1105–1131.

Fully nonlinear hyperbolic systems of partial differential equations related to plasticity

Communications in Partial Differential Equations, 20(7-8), 1133–1153.

The Riemann problem for a system of conservation laws of mixed type with a cubic nonlinearity

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 125(4), 675–699.

Traveling Wave Solutions of the Modified Korteweg-deVries-Burgers Equation

Journal of Differential Equations, 116(2), 448–467.

Formation and development of shear bands in granular material

Transactions of the 11th Army Conference on Applied Mathematics and Computing, 15–28. Research Triangle, North Carolina: Army Research Office.

Unloading near a shear band in granular material

Quarterly of Applied Mathematics, 52(3), 579–600.

Nonstrictly Hyperbolic Conservation Laws with a Parabolic Line

Journal of Differential Equations, 103(1), 94–126.

The Initial Value Problem for a System Modelling Unidirectional Longitudinal Elastic-Plastic Waves

SIAM Journal on Mathematical Analysis, 24(5), 1111–1144.

Unloading near a shear band: a free boundary problem for the wave equation

Communications in Partial Differential Equations, 18(7-8), 1271–1298.

Scale-invariant initial value problems in one-dimensional dynamic elastoplasticity, with consequences for multidimensional nonassociative plasticity

European Journal of Applied Mathematics, 3(3), 225–254.

Undercompressive shocks for nonstrictly hyperbolic conservation laws

Journal of Dynamics and Differential Equations, 3(2), 199–271.

Viscous Profiles and Numerical Methods for Shock Waves

Instability in Critical State Theories of Granular Flow

SIAM Journal on Applied Mathematics, 50(1), 33–47.

Loss of Hyperbolicity in Yield Vertex Plasticity Models under Nonproportional Loading

In The IMA Volumes in Mathematics and Its Applications (pp. 192–217).

Undercompressive Shocks in Systems of Conservation Laws

In The IMA Volumes in Mathematics and Its Applications (pp. 218–231).

Approximately periodic solutions of the elastic string equations

Applicable Analysis, 32(1), 1–14.

Loss of real characteristics for models of three-phase flow in a porous medium

Transport in Porous Media, 4(5).

Riemann problems involving undercompressive shocks

In M. Rascle, D. Serre, & M. Slemrod) (Eds.), PDEs and Continuum Models of Phase Transitions (pp. 187–200).

The Riemann problem for 2 × 2 systems of hyperbolic conservation laws with case I quadratic nonlinearities

Journal of Differential Equations, 80(2), 343–363.

The quasidynamic approximation in critical state plasticity

Archive for Rational Mechanics and Analysis, 108(4), 267–280.

Dynamic phase transitions in a van der Waals gas

Quarterly of Applied Mathematics, 46(4), 631–636.

Loss of strict hyperbolicity for the Buckley-Leverett equations of three phase flow in a porous medium

In M. Wheeler (Ed.), Numerical simulation in oil recovery. New York: Springer.

Phase jumps near the Maxwell line

Riemann problems for nonstrictly hyperbolic 2x2 systems of conservation laws

Transactions of the American Mathematical Society, 304(1), 267–306.

Solution of the riemann problem for a prototype 2x2 system of non-strictly hyperbolic conservation laws

Archive for Rational Mechanics and Analysis, 97(4), 299–320.

The classification of 2 × 2 systems of non-strictly hyperbolic conservation laws, with application to oil recovery

Communications on Pure and Applied Mathematics, 40(2), 141–178.

The elastic string equations: numerical results using Glimm’s method, and two new exact solutions

[CRSC Report]. Raleigh, North Carolina: NC State University.

Nonuniqueness of admissible solutions of Riemann initial value problems for a system of conservation laws of mixed type

Archive for Rational Mechanics and Analysis, 93(1), 45–59.

Recent developments in nonstrictly hyperbolic conservation laws

Transactions of the Fourth Army Conference on Applied Mathematics and Computing. Presented at the 4th Army Conference on Applied Mathematics and Computing, Cornell University, Ithaca, New York.

Shock waves and bifurcation

In L. Gama (Ed.), Proceedings of the Brazilian National Colloquium.

The Riemann problem for the planar motion of an elastic string

Journal of Differential Equations, 61(2), 149–163.

Three phase flow in porous media-recent developments in nonstrictly hyperbolic conservation laws

In G. Papanicolaou (Ed.), Advances in Multiphase Flow and Related Problems (pp. 210–218). Philadelphia, Pennsylvania: SIAM.

Elementary Wave Solutions of the Equations Describing the Motion of an Elastic String

SIAM Journal on Mathematical Analysis, 16(3), 447–459.

The interaction of transverse waves for the vibrating string

In J. H. Lightbourne & S. M. Rankin (Eds.), Physical Mathematics and Nonlinear Partial Differential Equations (pp. 229–238). New York: Marcel Dekker.

The nonlinear interaction of smooth travelling waves in an elastic string

Wave Motion, 7(2), 169–175.

Three phase flow in a porous medium and the classification of non-strictly hyperbolic conservation laws

Transactions of the third Army Conference on Applied Mathematics and Computing, 509–518. Research Triangle, North Carolina: U.S. Army Research Office.

Admissibility criteria for shock wave solutions of a system of conservation laws of mixed type

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 93(3-4), 233–244.

The Riemann problem for a class of conservation laws of mixed type

Journal of Differential Equations, 46(3), 426–443.

Coincident bifurcation of equilibrium and periodic solutions of evolution equations

Journal of Mathematical Analysis and Applications, 84(1), 113–132.

On Bifurcation and Symmetry in Benard Convection and Taylor Vortices

Studies in Applied Mathematics, 65(1), 85–93.

Bifurcation of axisymmetric buckled states of a thin spherical shell

Nonlinear Analysis: Theory, Methods & Applications, 4(4), 699–713.

One-parameter perturbations of bifurcation from a simple eigenvalue

Mathematical Proceedings of the Cambridge Philosophical Society, 88(1), 111–123.

Secondary Bifurcation Near a Double Eigenvalue

SIAM Journal on Mathematical Analysis, 11(2), 365–389.

Bifurcation in the neighbourhood of a non-isolated singular point

Israel Journal of Mathematics, 30(4), 363–381.

On the null spaces of linear Fredholm operators depending on several parameters

Mathematical Proceedings of the Cambridge Philosophical Society, 84(1), 131–142.

Secondary bifurcation for one-parameter families of bifurcation problems

(Report No. 97). Colchester, England: University of Essex.

Small solutions of a non-linear equation in Banach space for a degenerate case

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 79(1-2), 35–49.

Bifurcation from a multiple eigenvalue

In Ordinary and Partial Differential Equations (pp. 417–424).