2023 journal article

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

*JOURNAL OF FLUID MECHANICS*, *954*.

author keywords: suspensions; particle/fluid flow

Sources: ORCID, Web Of Science

Added: January 4, 2023

2021 article

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.

author keywords: asymptotic analysis; nonlinear waves; partial differential equations

Sources: ORCID, Web Of Science

Added: August 25, 2021

2020 journal article

Gradient-induced droplet motion over soft solids

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

author keywords: droplet motion; soft solids

Sources: Web Of Science, ORCID

Added: June 22, 2020

2019 journal article

Constitutive relations for compressible granular flow in the inertial regime

*JOURNAL OF FLUID MECHANICS*, *874*, 926–951.

author keywords: granular media; rheology

Sources: Web Of Science, ORCID

Added: August 12, 2019

2019 journal article

Distinguishing deformation mechanisms in elastocapillary experiments

*Soft Matter*, *15*(46), 9426–9436.

Source: ORCID

Added: November 20, 2019

2018 journal article

A SCALAR CONSERVATION LAW FOR PLUME MIGRATION IN CARBON SEQUESTRATION

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

author keywords: hyperbolic PDE; discontinuous flux; method of characteristics; shocks and rarefactions; residual trapping

Sources: Web Of Science, ORCID

Added: August 6, 2018

2018 journal article

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

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

author keywords: asymptotic analysis; nonlinear waves; partial differential equations

Sources: Web Of Science, ORCID, Crossref

Added: April 2, 2019

2018 journal article

Nonlocal rheology of dense granular flow in annular shear experiments

*Soft Matter*, *14*(16), 3040–3048.

Sources: Web Of Science, Crossref, ORCID

Added: August 6, 2018

2017 journal article

Deformation of an elastic substrate due to a resting sessile droplet

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

author keywords: PDEs in Connection with Mechanics of Deformable Solids; Transform Methods; Classical Linear Elasticity; Numerical Approximation of Solutions; Fluid-Solid Interactions

Sources: Web Of Science, Crossref, ORCID

Added: August 6, 2018

2017 journal article

Dispersive and Diffusive-Dispersive ShockWaves for Nonconvex Conservation Laws

*SIAM REVIEW*, *59*(1), 3–61.

author keywords: shock waves; conservation laws; partial differential equations; dispersive equations; traveling waves

Sources: Web Of Science, ORCID

Added: August 6, 2018

2017 journal article

Stationary Expansion Shocks for a Regularized Boussinesq System

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

Sources: Web Of Science, ORCID, Crossref

Added: August 6, 2018

2017 journal article

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.

author keywords: granular flow; continuum modelling; rheology

Sources: Web Of Science, ORCID, Crossref

Added: August 6, 2018

2017 journal article

Wetting dynamics of a collapsing fluid hole

*PHYSICAL REVIEW FLUIDS*, *2*(1).

Sources: Web Of Science, ORCID

Added: August 6, 2018

2016 journal article

Expansion shock waves in regularized shallow-water theory

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

author keywords: Lax entropy condition; non-local dispersion; Benjamin-Bona-Mahony equation; Boussinesq equations

Sources: Web Of Science, Crossref, ORCID

Added: August 6, 2018

2015 book

Partial differential equations: An introduction to theory and applications

Princeton: Princeton University Press.

Source: NC State University Libraries

Added: August 6, 2018

2015 journal article

Spatiotemporal measurement of surfactant distribution on gravity-capillary waves

*JOURNAL OF FLUID MECHANICS*, *777*.

author keywords: capillary waves; Faraday waves; waves/free-surface flows

Sources: Web Of Science, ORCID

Added: August 6, 2018

2015 article

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.

author keywords: Experiment; Model; Surfactant; Thin liquid film

Sources: Web Of Science, ORCID

Added: August 6, 2018

2015 journal article

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

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

Sources: Web Of Science, ORCID

Added: August 6, 2018

2014 journal article

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

*Soft Matter*, *10*(37), 7361.

Sources: NC State University Libraries, Crossref, ORCID

Added: August 6, 2018

2014 chapter book

Two Fluid Flow in a Capillary Tube

Sources: Web Of Science, ORCID, Crossref

Added: August 6, 2018

2013 journal article

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

*Applied Mathematics Research EXpress*, *7*.

Sources: Crossref, ORCID

Added: June 30, 2019

2013 conference paper

Two Fluid Flow in Porous Media

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

Source: NC State University Libraries

Added: July 28, 2019

2012 journal article

Simulation of spreading surfactant on a thin liquid film

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

author keywords: Thin liquid films; Surfactant; Hyperbolic-parabolic PDE; Numerical method

Sources: Crossref, ORCID

Added: June 30, 2019

2012 journal article

Stability of plane waves in two-phase porous media flow

*APPLICABLE ANALYSIS*, *91*(2), 295–308.

author keywords: two-phase flow; linear stability; shock waves

Sources: Web Of Science, ORCID

Added: August 6, 2018

2011 journal article

THE BUCKLEY-LEVERETT EQUATION WITH DYNAMIC CAPILLARY PRESSURE

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

author keywords: undercompressive shock; two-phase flow; porous medium; conservation law

Sources: Web Of Science, ORCID

Added: August 6, 2018

2010 journal article

Evolution of a Mixing Zone in Granular Avalanches

*Applied Mathematics Research EXpress*, *7*.

Sources: Crossref, ORCID

Added: June 30, 2019

2010 journal article

FINITE TIME EMERGENCE OF A SHOCK WAVE FOR SCALAR CONSERVATION LAWS

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

author keywords: Shock waves; conservation laws

Sources: Web Of Science, ORCID

Added: August 6, 2018

2010 journal article

Radial Spreading of a Surfactant on a Thin Liquid Film

*Applied Mathematics Research EXpress*, *9*.

Sources: Crossref, ORCID

Added: June 30, 2019

2010 journal article

SHOCK FORMATION AND BREAKING IN GRANULAR AVALANCHES

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

author keywords: avalanches; conservation laws; granular materials; segregation; shock waves

Sources: Web Of Science, ORCID

Added: August 6, 2018

2010 journal article

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

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

author keywords: Conservation laws; First order partial differential equations; Granular flow; Particle segregation

Sources: Web Of Science, ORCID, Crossref

Added: August 6, 2018

2010 journal article

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

*PHYSICAL REVIEW E*, *81*(5).

Sources: Web Of Science, ORCID

Added: August 6, 2018

2010 conference paper

The Gray-Thornton Model of Granular Segregation

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

Event: IUTAM-ISIMM SYMPOSIUM ON MATHEMATICAL MODELING AND PHYSICAL INSTANCES OF GRANULAR FLOWS

author keywords: Segregation; granular materials; shock waves; hyperbolic conservation laws

Sources: Crossref, ORCID

Added: January 8, 2019

2009 journal article

Periodic motion of a mass-spring system

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

author keywords: mass-spring system; Hamiltonian system; periodic solutions

Sources: Web Of Science, ORCID

Added: August 6, 2018

2009 other

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

Sources: NC State University Libraries, ORCID, Crossref

Added: August 6, 2018

2008 journal article

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

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

Sources: Web Of Science, ORCID

Added: August 6, 2018

2007 journal article

Automated Review of Prerequisite Material for Intermediate-Level Undergraduate Mathematics

*PRIMUS*, *17*(2), 167–180.

Sources: Crossref, ORCID

Added: June 30, 2019

2007 journal article

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

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

author keywords: granular materials; nonlinear hyperbolic partial differential equations

Sources: Web Of Science, ORCID

Added: August 6, 2018

2007 journal article

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

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

Sources: Web Of Science, ORCID, Crossref

Added: August 6, 2018

2006 journal article

Growing surfactant waves in thin liquid films driven by gravity

*Applied Mathematics Research EXpress*, *1*.

Sources: Crossref, ORCID

Added: June 30, 2019

2006 journal article

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

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

author keywords: PDE; surfactants; hyperbolic; parabolic system

Sources: Web Of Science, ORCID, Crossref

Added: August 6, 2018

2006 journal article

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.

author keywords: particle-size segregation; kinetic sieving; inverse-grading; shocks

Sources: Web Of Science, ORCID

Added: August 6, 2018

2005 journal article

Kinetics and nucleation for driven thin film flow

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

author keywords: kinetics; nucleation; Marangoni; Riemann solver; thin films; hyperbolic conservation laws; traveling waves

Sources: Web Of Science, ORCID, Crossref

Added: August 6, 2018

2005 article

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.

Sources: Web Of Science, ORCID

Added: August 6, 2018

2004 journal article

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

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

Sources: Web Of Science, ORCID, Crossref

Added: August 6, 2018

2004 journal article

Non-classical Riemann solvers with nucleation

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

Sources: Web Of Science, ORCID

Added: August 6, 2018

2003 journal article

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.

author keywords: shear band; stability; granular; discrete model

Sources: Web Of Science, ORCID

Added: August 6, 2018

2003 journal article

Thin film traveling waves and the Navier slip condition

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2002 journal article

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

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

Sources: Web Of Science, ORCID

Added: August 6, 2018

2001 journal article

A discrete model for an ill-posed nonlinear parabolic PDE

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

author keywords: nonlinear PDE; ill-posed equations; nonlinear diffusion; granular medium; shear bands

Sources: Web Of Science, ORCID

Added: August 6, 2018

2001 journal article

A nonconvex scalar conservation law with trilinear flux

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

Sources: Web Of Science, ORCID

Added: August 6, 2018

2001 journal article

Stability of compressive and undercompressive thin film travelling waves

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

Sources: Web Of Science, ORCID

Added: August 6, 2018

2000 journal article

Existence of undercompressive traveling waves in thin film equations

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

author keywords: undercompressive shocks; traveling waves; heteroclinic orbit; existence

Sources: Web Of Science, ORCID

Added: August 6, 2018

2000 journal article

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

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

Sources: Crossref, ORCID

Added: June 30, 2019

2000 journal article

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

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

Sources: Crossref, ORCID

Added: June 30, 2019

2000 journal article

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

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

Sources: Web Of Science, ORCID

Added: August 6, 2018

2000 other

Similarity solutions for granular flows in hoppers

Sources: Crossref, ORCID

Added: June 30, 2019

1999 journal article

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.

Sources: Web Of Science, ORCID

Added: August 6, 2018

1999 journal article

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

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

Sources: Web Of Science, ORCID

Added: August 6, 2018

1999 journal article

Undercompressive shocks in thin film flows

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

author keywords: undercompressive shock; capillarity; thin films; Marangoni stress; fourth order diffusion; numerical simulation; hyperbolic conservation law

Sources: Web Of Science, ORCID

Added: August 6, 2018

1999 chapter

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).

Ed(s): V. Alexiades & G. Siopsis

Sources: Crossref, ORCID

Added: July 10, 2019

1998 journal article

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

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

author keywords: plasticity; stress fluctuations; granular material

Sources: Web Of Science, ORCID

Added: August 6, 2018

1998 journal article

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.

Sources: Web Of Science, ORCID

Added: August 6, 2018

1998 journal article

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

*PHYSICAL REVIEW E*, *57*(2), 2053–2061.

Sources: Web Of Science, ORCID

Added: August 6, 2018

1998 journal article

Lithotripsy: The treatment of kidney stones with shock waves

*SIAM REVIEW*, *40*(2), 356–371.

author keywords: shock waves; bubble dynamics; asymptotic methods

Sources: Web Of Science, ORCID

Added: August 6, 2018

1997 chapter

Formation of Shear Bands in Models of Granular Materials

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

Sources: Crossref, ORCID

Added: September 14, 2020

1997 conference paper

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.

Ed(s): R. Behringer & J. Jenkins

Event: International Conference on Powders & Grains at Durham, North Carolina on May 18-23, 1997

Source: NC State University Libraries

Added: April 4, 2021

1997 journal article

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.

author keywords: plane shear waves; saturated granular material; hypoplastic flow rule; scale-invariant problem; characteristic wave; shock wave; rarefaction wave; wave curve; state space; kinetic energy

Sources: Web Of Science, ORCID

Added: August 6, 2018

1997 conference paper

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.

Ed(s): C. Chang, A. Misra, R. Liang & M. Babic

Source: NC State University Libraries

Added: April 4, 2021

1997 journal article

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.

Sources: Web Of Science, ORCID

Added: August 6, 2018

1996 conference paper

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.

Ed(s): J. Glimm, M. Graham, J. Grove & B. Plohr

Event: Fifth International Conference on Hyperbolic Problems at University of Stony Brook, New York on June 13-17, 1994

Source: NC State University Libraries

Added: November 24, 2021

1996 journal article

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

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

Sources: Crossref, ORCID

Added: January 24, 2021

1995 journal article

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

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

Sources: Crossref, ORCID

Added: September 7, 2020

1995 journal article

Fully nonlinear hyperbolic systems of partial differential equations related to plasticity

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

Sources: Crossref, ORCID

Added: September 14, 2020

1995 journal article

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.

Sources: Crossref, ORCID

Added: September 14, 2020

1995 journal article

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

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

Sources: Crossref, ORCID

Added: March 20, 2021

1994 conference paper

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.

Source: NC State University Libraries

Added: November 24, 2021

1994 journal article

Unloading near a shear band in granular material

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

Sources: Crossref, ORCID

Added: September 14, 2020

1993 journal article

Nonstrictly Hyperbolic Conservation Laws with a Parabolic Line

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

Sources: Crossref, ORCID

Added: September 14, 2020

1993 journal article

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

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

author keywords: ELASTOPLASTICITY; HYPERBOLIC EQUATIONS; FULLY NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS; INITIAL VALUE PROBLEM; WEAK SOLUTIONS

Sources: Crossref, ORCID

Added: September 14, 2020

1993 journal article

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

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

Sources: Crossref, ORCID

Added: September 14, 2020

1992 journal article

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.

Sources: Crossref, ORCID

Added: February 24, 2020

1991 journal article

Undercompressive shocks for nonstrictly hyperbolic conservation laws

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

Sources: Crossref, ORCID

Added: March 20, 2021

1991 report

Viscous Profiles and Numerical Methods for Shock Waves

Sources: Crossref, ORCID

Added: September 14, 2020

1990 journal article

Instability in Critical State Theories of Granular Flow

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

Sources: Crossref, ORCID

Added: September 14, 2020

1990 chapter

Loss of Hyperbolicity in Yield Vertex Plasticity Models under Nonproportional Loading

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

Sources: Crossref, ORCID

Added: September 14, 2020

1990 chapter

Undercompressive Shocks in Systems of Conservation Laws

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

Sources: Crossref, ORCID

Added: September 14, 2020

1989 journal article

Approximately periodic solutions of the elastic string equations

*Applicable Analysis*, *32*(1), 1–14.

Sources: Crossref, ORCID

Added: September 14, 2020

1989 journal article

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

*Transport in Porous Media*, *4*(5).

Sources: Crossref, ORCID

Added: September 14, 2020

1989 chapter

Riemann problems involving undercompressive shocks

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

Ed(s): M. Rascle, D. Serre & M. Slemrod)

Sources: Crossref, ORCID

Added: March 20, 2021

1989 journal article

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

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

Sources: Crossref, ORCID

Added: March 20, 2021

1989 journal article

The quasidynamic approximation in critical state plasticity

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

Sources: Crossref, ORCID

Added: September 14, 2020

1988 journal article

Dynamic phase transitions in a van der Waals gas

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

Sources: Crossref, ORCID

Added: September 14, 2020

1988 chapter

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.

Ed(s): M. Wheeler

Event: Symposium on Numerical Simulation in Oil Recovery at University of Minnesota

Source: NC State University Libraries

Added: November 24, 2021

1987 other

Phase jumps near the Maxwell line

Sources: Crossref, ORCID

Added: September 14, 2020

1987 journal article

Riemann problems for nonstrictly hyperbolic 2x2 systems of conservation laws

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

Sources: Crossref, ORCID

Added: March 20, 2021

1987 journal article

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.

Sources: Crossref, ORCID

Added: March 20, 2021

1987 journal article

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.

Sources: Crossref, ORCID

Added: March 20, 2021

1987 report

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

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

Source: NC State University Libraries

Added: November 24, 2021

1986 journal article

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.

Sources: Crossref, ORCID

Added: September 14, 2020

1986 conference paper

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.

Event: 4th Army Conference on Applied Mathematics and Computing at Cornell University, Ithaca, New York on May 27-31, 1986

Source: NC State University Libraries

Added: November 24, 2021

1986 conference paper

Shock waves and bifurcation

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

Ed(s): L. Gama

Source: NC State University Libraries

Added: November 24, 2021

1986 journal article

The Riemann problem for the planar motion of an elastic string

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

Sources: Crossref, ORCID

Added: September 14, 2020

1986 chapter

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.

Ed(s): G. Papanicolaou

Source: NC State University Libraries

Added: November 24, 2021

1985 journal article

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

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

Sources: Crossref, ORCID

Added: September 14, 2020

1985 chapter

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.

Ed(s): J. Lightbourne & S. Rankin

Source: NC State University Libraries

Added: November 24, 2021

1985 journal article

The nonlinear interaction of smooth travelling waves in an elastic string

*Wave Motion*, *7*(2), 169–175.

Sources: Crossref, ORCID

Added: September 14, 2020

1985 conference paper

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.

Event: Third Army Conference on Applied Mathematics and Computing at Atlanta, Georgia on May 13-16, 1985

Source: NC State University Libraries

Added: November 24, 2021

1983 journal article

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.

Sources: Crossref, ORCID

Added: September 14, 2020

1982 journal article

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

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

Sources: Crossref, ORCID

Added: September 14, 2020

1981 journal article

Coincident bifurcation of equilibrium and periodic solutions of evolution equations

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

Sources: Crossref, ORCID

Added: September 14, 2020

1981 journal article

On Bifurcation and Symmetry in Benard Convection and Taylor Vortices

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

Sources: Crossref, ORCID

Added: September 14, 2020

1980 journal article

Bifurcation of axisymmetric buckled states of a thin spherical shell

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

Sources: Crossref, ORCID

Added: September 14, 2020

1980 journal article

One-parameter perturbations of bifurcation from a simple eigenvalue

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

Sources: Crossref, ORCID

Added: September 14, 2020

1980 journal article

Secondary Bifurcation Near a Double Eigenvalue

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

Sources: Crossref, ORCID

Added: September 14, 2020

1978 journal article

Bifurcation in the neighbourhood of a non-isolated singular point

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

Sources: Crossref, ORCID

Added: March 20, 2021

1978 journal article

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

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

Sources: Crossref, ORCID

Added: September 14, 2020

1978 report

Secondary bifurcation for one-parameter families of bifurcation problems

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

Source: NC State University Libraries

Added: November 24, 2021

1977 journal article

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.

Sources: Crossref, ORCID

Added: January 24, 2021

1976 chapter

Bifurcation from a multiple eigenvalue

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

Sources: Crossref, ORCID

Added: September 14, 2020