The book summarizes several mathematical aspects of the vanishing viscosity method and considers its applications in studying dynamical systems such as dissipative systems, hyperbolic conversion systems and nonlinear dispersion systems. Including original research results, the book demonstrates how to use such methods to solve PDEs and is an essential reference for mathematicians, physicists and engineers working in nonlinear science.

Contents:

Preface

Sobolev Space and Preliminaries

The Vanishing Viscosity Method of Some Nonlinear Evolution System

The Vanishing Viscosity Method of Quasilinear Hyperbolic System

Physical Viscosity and Viscosity of Difference Scheme

Convergence of Lax–Friedrichs Scheme, Godunov Scheme and Glimm Scheme

Electric–Magnetohydrodynamic Equations

References