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# Nonlinear Evolutionary Partial Differential Equations

### About this Title

**Xia-Xi Ding** and **Tai-Ping Liu**, Editors

Publication: AMS/IP Studies in Advanced Mathematics

Publication Year:
1997; Volume 3

ISBNs: 978-0-8218-0661-6 (print); 978-1-4704-3794-7 (online)

DOI: https://doi.org/10.1090/amsip/003

MathSciNet review: MR1468477

MSC: Primary 35-06

### Table of Contents

**Front/Back Matter**

**Chapters**

- Multiscale structure for hyperbolic waves
- Euler-Poisson-Darboux equations and hyperbolic conservation laws
- Entropy for hyperbolic systems of conservation laws in several space dimensions
- Some results on nonlinear evolution equations
- The zero dispersion limit, a deterministic analogue of turbulence
- Nonlinear waves for viscous conservation laws
- Singular perturbation problems to a combustion equation in very long cylindrical domains
- Particle-like solutions of the Einstein-Yang Mills equations and the existence of an exotic black-hole solution
- The large time behavior of Cauchy problem for a dissipative Benjamin-Ono type equation
- Stability of boundary integral methods for water waves
- On the compactly supported solutions of KPP or Fischer type equations
- Delta waves in solutions of conservation laws
- Solution to M-D Riemann problems for quasilinear hyperbolic system of proportional conservation laws
- Contributions to the mathematical theory of magnetohydrodynamic shock waves
- Necessary and sufficient conditions of extinction and blow-up on some parabolic equations
- Analytic solutions of Belousov-Zhabotinskii reaction
- The global attractors for the Landau-Lifshitz equation of the ferromagnetic spin chain on compact manifolds
- Discontinuous solutions of the Navier-Stokes equations for multidimensional, compressible flow
- Global existence and qualitative behavior of solutions for the system of compressible adiabatic flow with damping
- Slow dynamics of linear waves in nonlinear systems of conservation laws
- A study of the global weak solution for the isentropic equation of a polytropic gas
- Smooth shock profiles in viscoelasticity with memory
- Weak linear degeneracy and global existence of classical solutions for quasilinear hyperbolic systems
- Survey of vacuum theory and conjecture
- The initial value problem of a system of conservation laws
- Entropy solutions for a hydrodynamic model for semiconductors
- A survey on stability of viscous shock profiles without genuine nonlinearity
- Asymptotic configuration of stationary interfacial patterns for reaction diffusion systems
- A symplectic difference scheme for the PDEs
- The essence of Glimm’s scheme
- Nonlinear Galerkin method using Legendre polynomials
- Multidimensional shock-waves for relativistic fluids
- Nonlinear system of equations of mixed type and nonlinear complex equation of mixed type
- On the stability of Broadwell shocks
- Riemann problem for hyperbolic combustion
- Optimal error estimates for viscosity method and monotone scheme to Riemann problem
- A new framework of nonlinear hydrodynamics
- Shock and boundary layer behavior of solutions to the Broadwell equation in the fluid dynamic limit
- A new proof of existence of the wave front solutions for a kind of reaction-diffusion system
- Resonances of the Schwarzschild metric
- Scattering operator for the Klein-Gordon equation on the Schwarzschild metric
- Periodic boundary value problem and Cauchy problem for generalized IMBq equation with several variables
- A degenerate reaction-diffusion problem
- Cauchy problem for strongly damped nonlinear wave equations
- Systems of quasilinear hyperbolic equations with quadratic coupling
- Large time step Glimm’s and Godunov’s schemes and their entropy consistency
- Nonlinear Galerkin method for Navier-Stokes equations with stream form
- A combined spectral-finite element method for a type of nonlinear two-dimensional Schrödinger equations
- Cauchy problem of nonisentropic gas dynamics equations
- Existence and uniqueness of global solution for certain degenerate reaction-diffusion systems
- On the spherically symmetric motion of self-gravitating isentropic gas surrounding a solid ball
- Dynamics on the attractor for reaction-diffusion systems in higher space dimensions
- Finite dimensionality of attractors of magnetic flow equation
- On a complex dynamical and dissipative structure of partial differential equations
- Global behavior of positive solutions to a quasilinear parabolic equation with nonlinear boundary absorption
- Interaction of three progressing waves with different singularities for semilinear wave equations
- The bidimensional Stefan problem with nonlinear convection
- Some problems on semiconductor equations
- Existence and nonexistence of global solution of nonlinear parabolic equation with nonlinear boundary condition
- Spirals for Riemann problems in multipieces for 2-D Euler equations by using MmB schemes
- Global existence of solutions for the reaction-diffusion systems which don’t satisfy a zero sum condition
- Nonexistence of global solutions to a class of generalized improved Boussinesq equations
- Zeros of solutions of hyperbolic equations with functional arguments
- Existence and convergence of solutions to higher order generalized KdV-Burgers equations
- Convergence and error bound analysis of a finite-difference scheme for the one-dimensional Navier-Stokes equations
- Vacuum problem for the damped p-system