Michael Shearer

Sprenger, P., Bridges, T. J., & Shearer, M. (2023). Traveling Wave Solutions of the Kawahara Equation Joining Distinct Periodic Waves. JOURNAL OF NONLINEAR SCIENCE, 33(5). https://doi.org/10.1007/s00332-023-09922-0

Barker, T., Gray, J. M. N. T., Schaeffer, D. G., & Shearer, M. (2023). Well-posedness and ill-posedness of single-phase models for suspensions. JOURNAL OF FLUID MECHANICS, 954. https://doi.org/10.1017/jfm.2022.1004

Congy, T., El, G. A., Hoefer, M. A., & Shearer, M. (2021, August 24). Dispersive Riemann problems for the Benjamin-Bona-Mahony equation. STUDIES IN APPLIED MATHEMATICS, Vol. 8. https://doi.org/10.1111/sapm.12426

Bardall, A., Chen, S.-Y., Daniels, K. E., & Shearer, M. (2020). Gradient-induced droplet motion over soft solids. IMA Journal of Applied Mathematics, 85(3), 495–512. https://doi.org/10.1093/imamat/hxaa015

Schaeffer, D. G., Barker, T., Tsuji, D., Gremaud, P., Shearer, M., & Gray, J. M. N. T. (2019). Constitutive relations for compressible granular flow in the inertial regime. JOURNAL OF FLUID MECHANICS, 874, 926–951. https://doi.org/10.1017/jfm.2019.476

Chen, S.-Y., Bardall, A., Shearer, M., & Daniels, K. E. (2019). Distinguishing deformation mechanisms in elastocapillary experiments. Soft Matter, 15(46), 9426–9436. https://doi.org/10.1039/C9SM01756A

Brown, E., & Shearer, M. (2018). A SCALAR CONSERVATION LAW FOR PLUME MIGRATION IN CARBON SEQUESTRATION. SIAM JOURNAL ON APPLIED MATHEMATICS, 78(3), 1823–1841. https://doi.org/10.1137/17m1127089

Congy, T., El, G. A., Hoefer, M. A., & Shearer, M. (2018). Nonlinear Schrödinger equations and the universal description of dispersive shock wave structure. Studies in Applied Mathematics, 142(3), 241–268. https://doi.org/10.1111/sapm.12247

Tang, Z., Brzinski, T. A., Shearer, M., & Daniels, K. E. (2018). Nonlocal rheology of dense granular flow in annular shear experiments. Soft Matter, 14(16), 3040–3048. https://doi.org/10.1039/c8sm00047f

Bardall, A., Daniels, K. E., & Shearer, M. (2017). Deformation of an elastic substrate due to a resting sessile droplet. European Journal of Applied Mathematics, 29(2), 281–300. https://doi.org/10.1017/s0956792517000134

El, G. A., Hoefer, M. A., & Shearer, M. (2017). Dispersive and Diffusive-Dispersive ShockWaves for Nonconvex Conservation Laws. SIAM REVIEW, 59(1), 3–61. https://doi.org/10.1137/15m1015650

Shearer, M., El, G. A., & Hoefer, M. A. (2017). Stationary Expansion Shocks for a Regularized Boussinesq System. Studies in Applied Mathematics, 139(4), 1–22. https://doi.org/10.1111/sapm.12191

Barker, T., Schaeffer, D. G., Shearer, M., & Gray, J. M. N. T. (2017). 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. https://doi.org/10.1098/rspa.2016.0846

Bostwick, J. B., Dijksman, J. A., & Shearer, M. (2017). Wetting dynamics of a collapsing fluid hole. PHYSICAL REVIEW FLUIDS, 2(1). https://doi.org/10.1103/physrevfluids.2.014006

El, G. A., Hoefer, M. A., & Shearer, M. (2016). Expansion shock waves in regularized shallow-water theory. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 472(2189), 20160141. https://doi.org/10.1098/rspa.2016.0141

Shearer, M., & Levy, R. (2015). Partial differential equations: An introduction to theory and applications. Princeton: Princeton University Press.

Strickland, S. L., Shearer, M., & Daniels, K. E. (2015). Spatiotemporal measurement of surfactant distribution on gravity-capillary waves. JOURNAL OF FLUID MECHANICS, 777. https://doi.org/10.1017/jfm.2015.352

Shearer, M., Spayd, K. R., & Swanson, E. R. (2015). Traveling waves for conservation laws with cubic nonlinearity and BBM type dispersion. JOURNAL OF DIFFERENTIAL EQUATIONS, 259(7), 3216–3232. https://doi.org/10.1016/j.jde.2015.04.019

Bostwick, J. B., Shearer, M., & Daniels, K. E. (2014). Elastocapillary deformations on partially-wetting substrates: rival contact-line models. Soft Matter, 10(37), 7361. https://doi.org/10.1039/C4SM00891J

Swanson, E. R., Strickland, S. L., Shearer, M., & Daniels, K. E. (2015, October). Surfactant spreading on a thin liquid film: reconciling models and experiments. JOURNAL OF ENGINEERING MATHEMATICS, Vol. 94, pp. 63–79. https://doi.org/10.1007/s10665-014-9735-0

Strait, M., Shearer, M., Levy, R., Cueto-Felgueroso, L., & Juanes, R. (2014). Two Fluid Flow in a Capillary Tube. https://doi.org/10.1007/978-3-319-11125-4_14

Shearer, M. (2013). Smooth Periodic Solutions of a 2x2 System of Nonlinear Hyperbolic Conservation Laws. Applied Mathematics Research EXpress, 7. https://doi.org/10.1093/amrx/abt006

Shearer, M. (2013). Two Fluid Flow in Porous Media. Proceedings of HYP2012, 8, 212–232. American Institute of Mathematical Sciences.

Peterson, E. R., & Shearer, M. (2012). Simulation of spreading surfactant on a thin liquid film. Applied Mathematics and Computation, 218(9), 5157–5167. https://doi.org/10.1016/j.amc.2011.11.002

Spayd, K., Shearer, M., & Hu, Z. (2012). Stability of plane waves in two-phase porous media flow. APPLICABLE ANALYSIS, 91(2), 295–308. https://doi.org/10.1080/00036811.2011.618128

Spayd, K., & Shearer, M. (2011). THE BUCKLEY-LEVERETT EQUATION WITH DYNAMIC CAPILLARY PRESSURE. SIAM JOURNAL ON APPLIED MATHEMATICS, 71(4), 1088–1108. https://doi.org/10.1137/100807016

McIntyre, M., Rowe, E. L., Shearer, M., Gray, J. M. N. T., & Thornton, A. R. (2010). Evolution of a Mixing Zone in Granular Avalanches. Applied Mathematics Research EXpress, 7. https://doi.org/10.1093/amrx/abm008

Shearer, M., & Dafermos, C. (2010). FINITE TIME EMERGENCE OF A SHOCK WAVE FOR SCALAR CONSERVATION LAWS. JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 7(1), 107–116. https://doi.org/10.1142/s0219891610002037

Peterson, E. R., & Shearer, M. (2010). Radial Spreading of a Surfactant on a Thin Liquid Film. Applied Mathematics Research EXpress, 9. https://doi.org/10.1093/amrx/abq015

Shearer, M., & Giffen, N. (2010). SHOCK FORMATION AND BREAKING IN GRANULAR AVALANCHES. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 27(2), 693–714. https://doi.org/10.3934/dcds.2010.27.693

May, L. B. H., Shearer, M., & Daniels, K. E. (2010). Scalar Conservation Laws with Nonconstant Coefficients with Application to Particle Size Segregation in Granular Flow. Journal of Nonlinear Science, 20(6), 689–707. https://doi.org/10.1007/s00332-010-9069-7

May, L. B. H., Golick, L. A., Phillips, K. C., Shearer, M., & Daniels, K. E. (2010). Shear-driven size segregation of granular materials: Modeling and experiment. PHYSICAL REVIEW E, 81(5). https://doi.org/10.1103/physreve.81.051301

Shearer, M., May, L. B. H., Giffen, N., Daniels, K. E., Goddard, J., Giovine, P., & Jenkins, J. T. (2010). The Gray-Thornton Model of Granular Segregation. Presented at the IUTAM-ISIMM SYMPOSIUM ON MATHEMATICAL MODELING AND PHYSICAL INSTANCES OF GRANULAR FLOWS. https://doi.org/10.1063/1.3435407

Shearer, M., Gremaud, P., & Kleiner, K. (2009). Periodic motion of a mass-spring system. IMA JOURNAL OF APPLIED MATHEMATICS, 74(6), 807–826. https://doi.org/10.1093/imamat/hxp032

Peterson, E., Shearer, M., Witelski, T. P., & Levy, R. (2009). Stability of traveling waves in thin liquid films driven by gravity and surfactant. https://doi.org/10.1090/psapm/067.2/2605281

Shearer, M., Gray, J. M. N. T., & Thornton, A. R. (2008). Stable solutions of a scalar conservation law for particle-size segregation in dense granular avalanches. EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 19, 61–86. https://doi.org/10.1017/S0956792507007280

Levy, R., Shearer, M., & Taylor, P. (2007). Automated Review of Prerequisite Material for Intermediate-Level Undergraduate Mathematics. PRIMUS, 17(2), 167–180. https://doi.org/10.1080/10511970601131555

Levy, R., Shearer, M., & Witelski, T. P. (2007). Gravity-driven thin liquid films with insoluble surfactant: smooth traveling waves. European Journal of Applied Mathematics, 18(6), 679–708. https://doi.org/10.1017/S0956792507007218

Schaeffer, D. G., Shearer, M., & Witelski, T. P. (2007). Boundary-value problems for hyperbolic equations related to steady granular flow. MATHEMATICS AND MECHANICS OF SOLIDS, 12(6), 665–699. https://doi.org/10.1177/1081286506067325

Witelski, T. P., Shearer, M., & Levy, R. (2006). Growing surfactant waves in thin liquid films driven by gravity. Applied Mathematics Research EXpress, 1. https://doi.org/10.1155/amrx/2006/15487

Levy, R., & Shearer, M. (2006). The Motion of a Thin Liquid Film Driven by Surfactant and Gravity. SIAM Journal on Applied Mathematics, 66(5), 1588–1609. https://doi.org/10.1137/050637030

Gray, J. M. N. T., Shearer, M., & Thornton, A. R. (2006). 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. https://doi.org/10.1098/rspa.2005.1580

Levy, R., & Shearer, M. (2005). Kinetics and nucleation for driven thin film flow. Physica D: Nonlinear Phenomena, 209(1-4), 145–163. https://doi.org/10.1016/j.physd.2005.07.003

Behringer, R. P., & Shearer, M. (2005, September 15). Non-linear dynamics of thin films and fluid interfaces - Preface. PHYSICA D-NONLINEAR PHENOMENA, Vol. 209, pp. VII-VIII. https://doi.org/10.1016/j.physd.2005.08.003

Shearer, M., & Schecter, S. (1989). Riemann problems involving undercompressive shocks. In M. Rascle, D. Serre, & M. Slemrod) (Eds.), PDEs and Continuum Models of Phase Transitions (pp. 187–200). https://doi.org/10.1007/bfb0024943

Levy, R., & Shearer, M. (2004). Comparison of two dynamic contact line models for driven thin liquid films. European Journal of Applied Mathematics, 15(6), 625–642. https://doi.org/10.1017/S0956792504005741

LeFloch, P. G., & Shearer, M. (2004). Non-classical Riemann solvers with nucleation. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 134(2004), 961–984. https://doi.org/10.1017/s0308210500003577

Shearer, M., Schaeffer, D. G., & Witelski, T. P. (2003). 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. https://doi.org/10.1142/S0218202503003069

Buckingham, R., Shearer, M., & Bertozzi, A. (2003). Thin film traveling waves and the Navier slip condition. SIAM Journal on Applied Mathematics, 63(2), 722–744. https://doi.org/10.1137/s0036139902401409

Segal, R. A., Martonen, T. B., Kim, C. S., & Shearer, M. (2002). Computer simulations of particle deposition in the lungs of chronic obstructive pulmonary disease patients. INHALATION TOXICOLOGY, 14(7), 705–720. https://doi.org/10.1080/08958370290084593

Witelski, T. P., Schaeffer, D. G., & Shearer, M. (2001). A discrete model for an ill-posed nonlinear parabolic PDE. PHYSICA D-NONLINEAR PHENOMENA, 160(3-4), 189–221. https://doi.org/10.1016/S0167-2789(01)00350-5

Hayes, B. T., & Shearer, M. (2001). A nonconvex scalar conservation law with trilinear flux. QUARTERLY OF APPLIED MATHEMATICS, 59(4), 615–635. https://doi.org/10.1090/qam/1866551

Bertozzi, A. L., Munch, A., Shearer, M., & Zumbrun, K. (2001). Stability of compressive and undercompressive thin film travelling waves. EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 12(2001 June), 253–291. https://doi.org/10.1017/s0956792501004466

Bertozzi, A. L., & Shearer, M. (2000). Existence of undercompressive traveling waves in thin film equations. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 32(1), 194–213. https://doi.org/10.1137/S0036141099350894

Segal, R. A., Guan, X., Shearer, M., & Martonen, T. B. (2000). Mathematical Model of Airflow in the Lungs of Children I: Effects of Tumor Sizes and Locations. Journal of Theoretical Medicine, 2(3), 199–213. https://doi.org/10.1080/10273660008833046

Guan, X., Segal, R. A., Shearer, M., & Martonen, T. B. (2000). Mathematical Model of Airflow in the Lungs of Children II: Effects of Ventilatory Parameters. Journal of Theoretical Medicine, 3(1), 51–62. https://doi.org/10.1080/10273660008833064

Gremaud, P. A., Schaeffer, D. G., & Shearer, M. (2000). Numerical determination of flow corrective inserts for granular materials in conical hoppers. INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 35(5), 869–882. https://doi.org/10.1016/S0020-7462(99)00064-5

Gremaud, P.-A., Matthews, J. V., & Shearer, M. (2000). Similarity solutions for granular flows in hoppers. https://doi.org/10.1090/conm/255/03975

Hayes, B., & Shearer, M. (1999). 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. https://doi.org/10.1017/s0308210500013111

Schulze, M. R., & Shearer, M. (1999). Undercompressive shocks for a system of hyperbolic conservation laws with cubic nonlinearity. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 229(1), 344–362. https://doi.org/10.1006/jmaa.1998.6186

Bertozzi, A. L., Munch, A., & Shearer, M. (1999). Undercompressive shocks in thin film flows. PHYSICA D-NONLINEAR PHENOMENA, 134(4), 431–464. https://doi.org/10.1016/s0167-2789(99)00134-7

Shearer, M., Bertozzi, A. L., & Munch, A. (1999). 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). https://doi.org/10.1090/amsip/013/04

Schaeffer, D. G., & Shearer, M. (1998). A simple model for stress fluctuations in plasticity with application to granular materials. SIAM JOURNAL ON APPLIED MATHEMATICS, 58(6), 1791–1807. https://doi.org/10.1137/S0036139996309746

Garaizar, F. X., Gordon, M., & Shearer, M. (1998). 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. https://doi.org/10.1006/jmaa.1997.5817

Schwarz, O. J., Horie, Y., & Shearer, M. (1998). Discrete element investigation of stress fluctuation in granular flow at high strain rates. PHYSICAL REVIEW E, 57(2), 2053–2061. https://doi.org/10.1103/physreve.57.2053

Howle, L., Schaeffer, D. G., Shearer, M., & Zhong, P. (1998). Lithotripsy: The treatment of kidney stones with shock waves. SIAM REVIEW, 40(2), 356–371. https://doi.org/10.1137/S0036144597322630

Shearer, M., Garaizar, F. X., & Gordon, M. K. (1997). Formation of Shear Bands in Models of Granular Materials. In IUTAM Symposium on Mechanics of Granular and Porous Materials (pp. 343–352). https://doi.org/10.1007/978-94-011-5520-5_31

Schaeffer, D. G., & Shearer, M. (1997). 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.

Gordon, M. S., Shearer, M., & Schaeffer, D. (1997). 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. https://doi.org/10.1016/S0020-7462(96)00080-7

Schaeffer, D. G., & Shearer, M. (1997). 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.

Schaeffer, D. G., & Shearer, M. (1997). 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. https://doi.org/10.1017/S0956792597003070

Shearer, M. (1996). 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.

Shearer, M., & Schaeffer, D. G. (1996). Riemann Problems for 5×5 Systems of Fully Non-linear Equations Related to Hypoplasticity. Mathematical Methods in the Applied Sciences, 19(18), 1433–1444. https://doi.org/10.1002/(sici)1099-1476(199612)19:18<1433::aid-mma824>3.0.co;2-x

Shearer, M., & Schaeffer, D. G. (1995). A class of fully nonlinear 2×2 systems of partial differential equations. Communications in Partial Differential Equations, 20(7-8), 1105–1131. https://doi.org/10.1080/03605309508821126

Shearer, M., & Schaeffer, D. G. (1995). Fully nonlinear hyperbolic systems of partial differential equations related to plasticity. Communications in Partial Differential Equations, 20(7-8), 1133–1153. https://doi.org/10.1080/03605309508821127

Shearer, M., & Yang, Y. (1995). 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. https://doi.org/10.1017/s0308210500030298

Jacobs, D., Mckinney, B., & Shearer, M. (1995). Traveling Wave Solutions of the Modified Korteweg-deVries-Burgers Equation. Journal of Differential Equations, 116(2), 448–467. https://doi.org/10.1006/jdeq.1995.1043

Shearer, M., Garaizar, F. X., Schaeffer, D. G., & Trangenstein, J. (1994). 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.

Shearer, M., & Schaeffer, D. G. (1994). Unloading near a shear band in granular material. Quarterly of Applied Mathematics, 52(3), 579–600. https://doi.org/10.1090/qam/1292207

Schaeffer, D. G., Schecter, S., & Shearer, M. (1993). Nonstrictly Hyperbolic Conservation Laws with a Parabolic Line. Journal of Differential Equations, 103(1), 94–126. https://doi.org/10.1006/jdeq.1993.1043

Shearer, M., & Schaeffer, D. G. (1993). The Initial Value Problem for a System Modelling Unidirectional Longitudinal Elastic-Plastic Waves. SIAM Journal on Mathematical Analysis, 24(5), 1111–1144. https://doi.org/10.1137/0524065

Schaeffer, D. G., & Shearer, M. (1993). Unloading near a shear band: a free boundary problem for the wave equation. Communications in Partial Differential Equations, 18(7-8), 1271–1298. https://doi.org/10.1080/03605309308820974

Schaeffer, D. G., & Shearer, M. (1992). 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. https://doi.org/10.1017/S0956792500000814

Schecter, S., & Shearer, M. (1991). Undercompressive shocks for nonstrictly hyperbolic conservation laws. Journal of Dynamics and Differential Equations, 3(2), 199–271. https://doi.org/10.1007/bf01047709

Shearer, M. (1991). Viscous Profiles and Numerical Methods for Shock Waves. https://doi.org/10.21236/ada246110

Schaeffer, D. G., Shearer, M., & Pitman, E. B. (1990). Instability in Critical State Theories of Granular Flow. SIAM Journal on Applied Mathematics, 50(1), 33–47. https://doi.org/10.1137/0150003

Schaeffer, D. G., & Shearer, M. (1990). Loss of Hyperbolicity in Yield Vertex Plasticity Models under Nonproportional Loading. In The IMA Volumes in Mathematics and Its Applications (pp. 192–217). https://doi.org/10.1007/978-1-4613-9049-7_15

Shearer, M., & Schecter, S. (1990). Undercompressive Shocks in Systems of Conservation Laws. In The IMA Volumes in Mathematics and Its Applications (pp. 218–231). https://doi.org/10.1007/978-1-4613-9049-7_16

Fehribach, J. D., & Shearer, M. (1989). Approximately periodic solutions of the elastic string equations. Applicable Analysis, 32(1), 1–14. https://doi.org/10.1080/00036818908839835

Shearer, M., & Trangenstein, J. A. (1989). Loss of real characteristics for models of three-phase flow in a porous medium. Transport in Porous Media, 4(5). https://doi.org/10.1007/bf00179533

Shearer, M. (1989). The Riemann problem for 2 × 2 systems of hyperbolic conservation laws with case I quadratic nonlinearities. Journal of Differential Equations, 80(2), 343–363. https://doi.org/10.1016/0022-0396(89)90088-0

Shearer, M., & Schaeffer, D. G. (1989). The quasidynamic approximation in critical state plasticity. Archive for Rational Mechanics and Analysis, 108(4), 267–280. https://doi.org/10.1007/bf01052974

Shearer, M. (1988). Dynamic phase transitions in a van der Waals gas. Quarterly of Applied Mathematics, 46(4), 631–636. https://doi.org/10.1090/qam/973380

Shearer, M. (1988). 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.

Shearer, M. (1987). Phase jumps near the Maxwell line. https://doi.org/10.1090/conm/060/873536

Schaeffer, D. G., & Shearer, M. (1987). Riemann problems for nonstrictly hyperbolic 2x2 systems of conservation laws. Transactions of the American Mathematical Society, 304(1), 267–306. https://doi.org/10.1090/s0002-9947-1987-0906816-5

Shearer, M., Schaeffer, D. G., Marchesin, D., & Paes-Leme, P. L. (1987). 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. https://doi.org/10.1007/bf00280409

Schaeffer, D. G., & Shearer, M. (1987). 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. https://doi.org/10.1002/cpa.3160400202

Shearer, M., & Fehribach, J. (1987). The elastic string equations: numerical results using Glimm’s method, and two new exact solutions [CRSC Report]. Raleigh, North Carolina: NC State University.

Shearer, M. (1986). 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. https://doi.org/10.1007/bf00250844

Shearer, M., & Schaeffer, D. G. (1986). 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.

Shearer, M. (1986). Shock waves and bifurcation. In L. Gama (Ed.), Proceedings of the Brazilian National Colloquium.

Shearer, M. (1986). The Riemann problem for the planar motion of an elastic string. Journal of Differential Equations, 61(2), 149–163. https://doi.org/10.1016/0022-0396(86)90116-6

Shearer, M., & Schaeffer, D. G. (1986). 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.

Shearer, M. (1985). Elementary Wave Solutions of the Equations Describing the Motion of an Elastic String. SIAM Journal on Mathematical Analysis, 16(3), 447–459. https://doi.org/10.1137/0516032

Shearer, M. (1985). 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.

Shearer, M. (1985). The nonlinear interaction of smooth travelling waves in an elastic string. Wave Motion, 7(2), 169–175. https://doi.org/10.1016/0165-2125(85)90044-7

Shearer, M., & Schaeffer, D. G. (1985). 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.

Shearer, M. (1983). 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. https://doi.org/10.1017/s0308210500015948

Shearer, M. (1982). The Riemann problem for a class of conservation laws of mixed type. Journal of Differential Equations, 46(3), 426–443. https://doi.org/10.1016/0022-0396(82)90103-6

Shearer, M. (1981). Coincident bifurcation of equilibrium and periodic solutions of evolution equations. Journal of Mathematical Analysis and Applications, 84(1), 113–132. https://doi.org/10.1016/0022-247x(81)90154-2

Shearer, M., & Walton, I. C. (1981). On Bifurcation and Symmetry in Benard Convection and Taylor Vortices. Studies in Applied Mathematics, 65(1), 85–93. https://doi.org/10.1002/sapm198165185

Shearer, M. (1980). Bifurcation of axisymmetric buckled states of a thin spherical shell. Nonlinear Analysis: Theory, Methods & Applications, 4(4), 699–713. https://doi.org/10.1016/0362-546x(80)90070-x

Shearer, M. (1980). One-parameter perturbations of bifurcation from a simple eigenvalue. Mathematical Proceedings of the Cambridge Philosophical Society, 88(1), 111–123. https://doi.org/10.1017/s0305004100057388

Shearer, M. (1980). Secondary Bifurcation Near a Double Eigenvalue. SIAM Journal on Mathematical Analysis, 11(2), 365–389. https://doi.org/10.1137/0511034

Shearer, M. (1978). Bifurcation in the neighbourhood of a non-isolated singular point. Israel Journal of Mathematics, 30(4), 363–381. https://doi.org/10.1007/bf02762000

Shearer, M. (1978). On the null spaces of linear Fredholm operators depending on several parameters. Mathematical Proceedings of the Cambridge Philosophical Society, 84(1), 131–142. https://doi.org/10.1017/s0305004100054979

Shearer, M. (1978). Secondary bifurcation for one-parameter families of bifurcation problems (Report No. 97). Colchester, England: University of Essex.

Shearer, M. (1977). 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. https://doi.org/10.1017/s0308210500016802

Shearer, M. (1976). Bifurcation from a multiple eigenvalue. In Ordinary and Partial Differential Equations (pp. 417–424). https://doi.org/10.1007/bfb0087360