**AMS/IP Studies in Advanced Mathematics**

Volume: 3;
1997;
637 pp;
Softcover

MSC: Primary 35; 58; 14;
Secondary 76; 32; 81

Print ISBN: 978-0-8218-0661-6

Product Code: AMSIP/3

List Price: $89.00

AMS Member Price: $71.20

MAA Member Price: $80.10

**Electronic ISBN: 978-1-4704-3794-7
Product Code: AMSIP/3.E**

List Price: $89.00

AMS Member Price: $71.20

MAA Member Price: $80.10

# Nonlinear Evolutionary Partial Differential Equations

Share this page *Edited by *
*Xia-Xi Ding; Tai-Ping Liu*

A co-publication of the AMS and International Press of Boston

This volume contains the proceedings from the International Conference on Nonlinear Evolutionary Partial Differential Equations held in Beijing in June 1993. The topic for the conference was selected because of its importance in the natural sciences and for its mathematical signifcance. Discussion topics include conservation laws, dispersion waves, Einstein's theory of gravitation, reaction-diffusion equations, the Navier-Stokes equations, and more. New results were presented and are featured in this volume.

Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.

#### Readership

Graduate students and research mathematicians interested in algebraic geometry.

# Table of Contents

## Nonlinear Evolutionary Partial Differential Equations

- Cover Cover11
- Title page v6
- Contents vii8
- Preface xiii14
- Multiscale structure for hyperbolic waves 116
- Euler-Poisson-Darboux equations and hyperbolic conservation laws 1126
- Entropy for hyperbolic systems of conservation laws in several space dimensions 2742
- Some results on nonlinear evolution equations 4358
- The zero dispersion limit, a deterministic analogue of turbulence 5368
- Nonlinear waves for viscous conservation laws 6580
- Singular perturbation problems to a combustion equation in very long cylindrical domains 7590
- Particle-like solutions of the Einstein-Yang Mills equations and the existence of an exotic black-hole solution 85100
- The large time behavior of Cauchy problem for a dissipative Benjamin-Ono type equation 91106
- Stability of boundary integral methods for water waves 107122
- On the compactly supported solutions of KPP or Fischer type equations 129144
- Delta waves in solutions of conservation laws 139154
- Solution to M-D Riemann problems for quasilinear hyperbolic system of proportional conservation laws 157172
- Contributions to the mathematical theory of magnetohydrodynamic shock waves 175190
- Necessary and sufficient conditions of extinction and blow-up on some parabolic equations 189204
- Analytic solutions of Belousov-Zhabotinskii reaction 199214
- The global attractors for the Landau-Lifshitz equation of the ferromagnetic spin chain on compact manifolds 213228
- Discontinuous solutions of the Navier-Stokes equations for multidimensional, compressible flow 229244
- Global existence and qualitative behavior of solutions for the system of compressible adiabatic flow with damping 237252
- Slow dynamics of linear waves in nonlinear systems of conservation laws 247262
- A study of the global weak solution for the isentropic equation of a polytropic gas 261276
- Smooth shock profiles in viscoelasticity with memory 271286
- Weak linear degeneracy and global existence of classical solutions for quasilinear hyperbolic systems 283298
- Survey of vacuum theory and conjecture 293308
- The initial value problem of a system of conservation laws 307322
- Entropy solutions for a hydrodynamic model for semiconductors 311326
- A survey on stability of viscous shock profiles without genuine nonlinearity 319334
- Asymptotic configuration of stationary interfacial patterns for reaction diffusion systems 333348
- A symplectic difference scheme for the PDEs 349364
- The essence of Glimm’s scheme 355370
- Nonlinear Galerkin method using Legendre polynomials 363378
- Multidimensional shock-waves for relativistic fluids 377392
- Nonlinear system of equations of mixed type and nonlinear complex equation of mixed type 393408
- On the stability of Broadwell shocks 403418
- Riemann problem for hyperbolic combustion 413428
- Optimal error estimates for viscosity method and monotone scheme to Riemann problem 419434
- A new framework of nonlinear hydrodynamics 433448
- Shock and boundary layer behavior of solutions to the Broadwell equation in the fluid dynamic limit 455470
- A new proof of existence of the wave front solutions for a kind of reaction-diffusion system 469484
- Resonances of the Schwarzschild metric 483498
- Scattering operator for the Klein-Gordon equation on the Schwarzschild metric 489504
- Periodic boundary value problem and Cauchy problem for generalized IMBq equation with several variables 495510
- A degenerate reaction-diffusion problem 501516
- Cauchy problem for strongly damped nonlinear wave equations 505520
- Systems of quasilinear hyperbolic equations with quadratic coupling 509524
- Large time step Glimm’s and Godunov’s schemes and their entropy consistency 515530
- Nonlinear Galerkin method for Navier-Stokes equations with stream form 521536
- A combined spectral-finite element method for a type of nonlinear two-dimensional Schrödinger equations 527542
- Cauchy problem of nonisentropic gas dynamics equations 533548
- Existence and uniqueness of global solution for certain degenerate reaction-diffusion systems 537552
- On the spherically symmetric motion of self-gravitating isentropic gas surrounding a solid ball 543558
- Dynamics on the attractor for reaction-diffusion systems in higher space dimensions 547562
- Finite dimensionality of attractors of magnetic flow equation 553568
- On a complex dynamical and dissipative structure of partial differential equations 559574
- Global behavior of positive solutions to a quasilinear parabolic equation with nonlinear boundary absorption 565580
- Interaction of three progressing waves with different singularities for semilinear wave equations 571586
- The bidimensional Stefan problem with nonlinear convection 577592
- Some problems on semiconductor equations 583598
- Existence and nonexistence of global solution of nonlinear parabolic equation with nonlinear boundary condition 589604
- Spirals for Riemann problems in multipieces for 2-D Euler equations by using MmB schemes 595610
- Global existence of solutions for the reaction-diffusion systems which don’t satisfy a zero sum condition 601616
- Nonexistence of global solutions to a class of generalized improved Boussinesq equations 607622
- Zeros of solutions of hyperbolic equations with functional arguments 613628
- Existence and convergence of solutions to higher order generalized KdV-Burgers equations 619634
- Convergence and error bound analysis of a finite-difference scheme for the one-dimensional Navier-Stokes equations 625640
- Vacuum problem for the damped p-system 633648
- Back Cover Back Cover1653