Quasilinear Hyperbolic Systems and Dissipative Mechanisms

Quasilinear Hyperbolic Systems and Dissipative Mechanisms
ISBN-10
9814497185
ISBN-13
9789814497183
Category
Mathematics
Pages
232
Language
English
Published
1998-02-24
Publisher
World Scientific
Author
L Hsiao

Description

This book introduces the recent developments in the subject of quasilinear hyperbolic systems with dissipation, such as frictional damping, relaxation, viscosity and heat diffusion. The mathematical theory behind this subject is emphasized in two ways. One emphasis is based on understanding the influence of the dissipation mechanism on the qualitative behavior of solutions, such as the nonlinear diffusive phenomena caused by damping, and other phenomena (including phase transition) for the case with viscosity and heat diffusion. The second emphasis is to take the systems with the dissipation mechanism as an approach to approximating the corresponding system of quasilinear hyperbolic conservation laws – the zero-limit relaxation, or the zero-limit viscosity, and the related topic of nonlinear stability of waves. Contents:Frictional Damping: Globally Defined Classical Solutions and Their Nonlinear Diffusive PhenomenaFrictional Damping: Globally Defined Weak Solutions and The Nonlinear Diffusive PhenomenaRelaxationThe Influence of Dissipation Mechanism on the Qualitative Behavior of SolutionsVanishing Viscosity and Nonlinear Stability of Waves Readership: Postgraduate students, mathematicians, physicists and engineers in theoretical and numerical analysis of partial differentiation equations and continuum mechanics. keywords:Problem of Vanishing Viscosity;Relaxation;Dissipation;Large-Time Behaviour;Nonlinear Stability;Zero Relaxation Limit

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