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
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