**Contemporary Mathematics**

Volume: 526;
2010;
389 pp;
Softcover

MSC: Primary 35; 39; 65;

Print ISBN: 978-0-8218-4976-7

Product Code: CONM/526

List Price: $115.00

Individual Member Price: $92.00

**Electronic ISBN: 978-0-8218-8205-4
Product Code: CONM/526.E**

List Price: $115.00

Individual Member Price: $92.00

# Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena

Share this page *Edited by *
*Helge Holden; Kenneth H. Karlsen*

This volume presents the state of the art in several directions of research conducted by renowned mathematicians who participated in the research program on Nonlinear Partial Differential Equations at the Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway, during the academic year 2008–09.

The main theme of the volume is nonlinear partial differential equations that model a wide variety of wave phenomena. Topics discussed include systems of conservation laws, compressible Navier-Stokes equations, Navier-Stokes-Korteweg type systems in models for phase transitions, nonlinear evolution equations, degenerate/mixed type equations in fluid mechanics and differential geometry, nonlinear dispersive wave equations (Korteweg-de Vries, Camassa-Holm type, etc.), and Poisson interface problems and level set formulations.

#### Table of Contents

# Table of Contents

## Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena

- Contents v6 free
- Preface vii8 free
- A hyperbolic model of granular flow 110 free
- Hilbertian approaches to some non-linear conservation laws 1928
- On the asymptotic behavior of the gradient flow of a polyconvex functional 3746
- On degenerate partial differential equations 5362
- Symmetric solutions to multi-dimensional conservation laws 91100
- Product estimates for wave-Sobolev spaces in 2 + 1 and 1 + 1 dimensions 125134
- On the Cauchy problem for the modified Korteweg-de Vries equation with steplike finite-gap initial data 151160
- Asymptotic analysis in thermodynamics of viscous fluids 159168
- Well-posedness and blow-up phenomena for a modified two-component Camassa-Holm equation 199208
- Instability of solitary waves for a nonlinearly dispersive equation 221230
- Kinetic relations for undercompressive shock waves. Physical, mathematical,and numerical issues 237246
- Global regularity, and wave breaking phenomena in a class of nonlocaldispersive equations 273282
- Potential based, constraint preserving, genuinely multi-dimensional schemes for systems of conservation laws 295304
- A local and low-order Navier-Stokes-Korteweg system 315324
- Local existence for viscous system of conservation laws: Hs-data with s > 1 + d/2 339348
- Finite difference methods for discretizing singular source terms in a Poisson interface problem 359368

#### Readership

Graduate students and research mathematicians interested in partial differental equations and nonlinear analysis.