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Nonlinear Evolutionary Partial Differential Equations
Edited by: Xia-Xi Ding, Academia Sinica, Beijing, China, and Tai-Ping Liu, Stanford University, CA
A co-publication of the AMS and International Press.
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AMS/IP Studies in Advanced Mathematics
1997; 637 pp; softcover
Volume: 3
ISBN-10: 0-8218-0661-0
ISBN-13: 978-0-8218-0661-6
List Price: US$84
Member Price: US$67.20
Order Code: AMSIP/3
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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, Cambridge, MA.

Readership

Graduate students and research mathematicians interested in algebraic geometry.

Table of Contents

Plenary Lectures
  • B. Boston, J. Glimm, J. W. Grove, R. Holmes, and Q. Zhang -- Multiscale structure for hyperbolic waves
  • G.-Q. Chen -- Euler-Poisson-Darboux equations and hyperbolic conservation laws
  • C. M. Dafermos -- Entropy for hyperbolic systems of conservation laws in several space dimensions
  • X.-X. Ding -- Some results on nonlinear evolution equations
  • P. D. Lax -- The zero dispersion limit, a deterministic analogue of turbulence
  • T.-P. Liu -- Nonlinear waves for viscous conservation laws
  • M. Mimura, K. Sakamoto, and S.-I. Ei -- Singular perturbation problems to a combustion equation in very long cylindrical domains
  • J. A. Smoller and A. G. Wasserman -- Particle-like solutions of the Einstein-Yang-Mills equations and the existence of an exotic black-hole solution
  • Y. Zhou and B. Guo -- The large time behavior of Cauchy problems for a dissipative Benjamin-Ono type equation
Parallel Invited Talks
  • J. T. Beale, T. Y. Hou, and J. Lowengrub -- Stability of boundary integral methods for water waves
  • Z. Biro and R. Kersner -- On the compactly supported solutions of KPP or Fischer type equations
  • T. Chang and S. Yang -- Delta waves in solutions of conservation laws
  • C. Shuxing -- Solution to M-D Riemann problems for quasilinear hyperbolic system of proportional conservation laws
  • H. Freistühler -- Contributions to the mathematical theory of magnetohydrodynamic shock waves
  • Y. Gu -- Necessary and sufficient conditions of extinction and blow-up on some parabolic equations
  • G. Ben-Yu and C. Zhi-Xiong -- Analytic solutions of Belousov-Zhabotinskii reaction
  • G. Boling, H. Min-chun, and S. Fengqiu -- The global attractors for the Landau-Lifshitz equation of the Ferromagnetic spin chain on compact manifolds
  • D. Hoff -- Discontinuous solutions of the Navier-Stokes equations for multidimensional, compressible flow
  • L. Hsiao -- Global existence and qualitative behavior of solutions for the system of compressible adiabatic flow with damping
  • F. Hubert and D. Serre -- Slow dynamics of linear waves in nonlinear systems of conservation laws
  • A. Jeffrey and Y. G. Lu -- A study of the global weak solution for the isentropic equations of a polytropic gas
  • S. Kawashima and H. Hattori -- Smooth shock profiles in viscoelasticity with memory
  • L. Ta-tsien, Z. Yi, and K. De-xing -- Weak linear degeneracy and global existence of classical solutions for quasilinear hyperbolic systems
  • L. Lin -- Survey of vacuum theory and conjecture
  • P. Luo -- The initial value problem of a system of conservation laws
  • P. A. Marcati and R. Natalini -- Entropy solutions for a hydrodynamic model for semiconductors
  • A. Matsumura -- A survey on stability of viscous shock profiles without genuine nonlinearity
  • Y. Nishiura and H. Suzuki -- Asymptotic configuration of stationary interfacial patterns for reaction diffusion systems
  • Q. Mengzhao -- A symplectic difference scheme for the PDEs
  • S. Schochet -- The essence of Glimm's scheme
  • J. Shen and R. Temam -- Nonlinear Galerkin method using Legendre polynomials
  • J. Smoller and B. Temple -- Multi-dimensional shock-waves for relativistic fluids
  • S. Hesheng -- Nonlinear system of equations of mixed type and nonlinear complex equation of mixed type
  • A. Szepessy -- On the stability of Broadwell shocks
  • D. Tan -- Riemann problem for hyperbolic combustion
  • T. Zhen-huan -- Optimal error estimates for viscosity method and monotone scheme to Riemann problem
  • J. Wu -- A new framework of nonlinear hydrodynamics
  • Z. Xin -- Shock and boundary layer behavior of solutions to the Broadwell equation in the fluid dynamic limit
  • Z. Li and Y. I. Kanel -- A new proof of existence of the wave front solutions for a kind of reaction-diffusion system
Contributions
  • A. Motet-Bachelot -- Resonances of the Schwarzschild metric
  • A. Bachelot -- Scattering operator for the Klein-Gordon equation on the Schwarzschild metric
  • G. Chen and Z. Yang -- Periodic boundary value problem and Cauchy problem for generalized IMBq equation with several variables
  • Z. Chen and X. Chen -- A degenerate reaction-diffusion problem
  • E. Fan and Y. Wang -- Cauchy problem for strongly damped nonlinear wave equations
  • B. Hanouzet and R. Natalini -- Systems of quasilinear hyperbolic equations with quadratic coupling
  • J. Huang -- Large time step Glimm's and Godunov's schemes and their entropy consistency
  • L. Kaitai, M. Yichen, and F. Weibing -- Nonlinear Galerkin method for Navier-Stokes equations with stream form
  • X.-Q. Liu and S.-C. Wu -- A combined spectral-finite element method for a type of nonlinear two-dimensional Schrödinger equation
  • L. Fagui -- Cauchy problem of nonisentropic gas dynamics equations
  • L. Guo-fu -- Existence and uniqueness of global solution for certain degenerate reaction-diffusion systems
  • T. Makino -- On the spherically symmetric motion of self-gravitating isentropic gas surrounding a solid ball
  • Y. Morita -- Dynamics on the attractor for reaction-diffusion systems in higher space dimensions
  • Q. Chaochun and C. Fengxin -- Finite dimensionality of attractors of magnetic flow equation
  • S. K. Ng -- On a complex dynamical and dissipative structure of partial differential equations
  • M.-X. Wang -- Global behavior of positive solutions to quasilinear parabolic equation with nonlinear boundary absorption
  • W. Weike -- Interaction of three progressing waves with different singularities for semilinear wave equations
  • W. Xuefeng -- The bidimensional Stefan problem with nonlinear convection
  • W. Yuanming and G. Ping -- Some problems on semiconductor equations
  • W. Yong-hui and W. Ming-Xin -- Existence and nonexistence of global solution of nonlinear parabolic equation with nonlinear boundary condition
  • S. Yang -- Spirals for Riemann problems in multipieces for 2-D Euler equations by using MmB schemes
  • Y. Wanli -- Global existence of solutions for the reaction-diffusion systems which don't satisfy a zero sum condition
  • Z. Yang and G. Chen -- Nonexistence of global solutions to a class of generalized improved Boussinesq equations
  • N. Yoshida -- Zeros of solutions of hyperbolic equations with functional arguments
  • H. Zhao, C. Zhu, and Z. Yu -- Existence and convergence of solutions to higher order generalized KDV-Burgers equations
  • J. J. Zhao and D. Hoff -- Convergence and error bound analysis of a finite-difference scheme for the one-dimensional Navier-Stokes equations
  • Y.-S. Zheng -- Vacuum problem for the damped p-system
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