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Nonlinear PDE's, Dynamics and Continuum Physics
Edited by: Jerry Bona, University of Texas, Austin, TX, Katarzyna Saxton, Loyola University, New Orleans, LA, and Ralph Saxton, University of New Orleans, LA
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Contemporary Mathematics
2000; 256 pp; softcover
Volume: 255
ISBN-10: 0-8218-1052-9
ISBN-13: 978-0-8218-1052-1
List Price: US$75
Member Price: US$60
Order Code: CONM/255
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This volume contains the refereed proceedings of the conference on Nonlinear Partial Differential Equations, Dynamics and Continuum Physics which was held at Mount Holyoke College in Massachusetts, from July 19th to July 23rd, 1998. Models examined derive from a wide range of applications, including elasticity, thermoviscoelasticity, granular media, fluid dynamics, gas dynamics and conservation laws. Mathematical topics include existence theory and stability/instability of traveling waves, asymptotic behavior of solutions to nonlinear wave equations, effects of dissipation, mechanisms of blow-up, well-posedness and regularity, and fractal solutions.

The text will be of interest to graduate students and researchers working in nonlinear partial differential equations and applied mathematics.

Readership

Graduate students and researchers interested in partial differential equations and applied mathematics.

Table of Contents

  • H. Chen -- Travelling-waves for generalized KdV-Burgers equations
  • S. R. Choudhury -- Some analytical coherent structures of the long-wave equations
  • W. Domański -- Weakly nonlinear elastic plane waves in a cubic crystal
  • M. L. Frankel and V. Roytburd -- On dynamics of exothermic interfaces
  • P.-A. Gremaud, J. V. Matthews, and M. Shearer -- Similarity solutions for granular flows in hoppers
  • T. Hagen and M. Renardy -- Stability issues in nonisothermal elongational flow
  • L. Hsiao and R. Pan -- The damped \(P\)-system with boundary effects
  • B. L. Keyfitz and C. A. Mora -- Prototypes for nonstrict hyperbolicity in conservation laws
  • S. Kichenassamy -- Stability of blow-up patterns for nonlinear wave equations
  • M. Kovalyov -- Slowly decaying solutions of KdV
  • I. Rodnianski -- Fractal solutions of the Schrödinger equation
  • J. Shatah and W. Strauss -- Spectral condition for abstract instability
  • A. Tovbis -- On approximation of stable and unstable manifolds and the Stokes phenomenon
  • S. J. Watson -- A priori bounds in one-dimensional nonlinear thermoviscoelasticity
  • R. Young -- Periodic solutions to conservation laws
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