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Hyperbolic and Viscous Conservation Laws

Hyperbolic and Viscous Conservation Laws

$62.00

Part of CBMS-NSF Regional Conference Series in Applied Mathematics

  • Date Published: September 1999
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9780898714364

$ 62.00
Paperback

This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
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About the Authors
  • Here is an in-depth, up-to-date analysis of wave interactions for general systems of hyperbolic and viscous conservation laws. This self-contained study of shock waves explains the new wave phenomena from both a physical and a mathematical standpoint. The analysis is useful for the study of various physical situations, including nonlinear elasticity, magnetohydrodynamics, multiphase flows, combustion, and classical gas dynamics shocks. The central issue throughout the book is the understanding of nonlinear wave interactions. The book describes the qualitative theory of shock waves. It begins with the basics of the theory for scalar conservation law and Lax's solution of the Reimann problem. For hyperbolic conservation laws, the Glimm scheme and wave tracing techniques are presented and used to study the regularity and large-time behavior of solutions. Viscous nonlinear waves are studied via the recent approach to pointwise estimates.

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    Product details

    • Date Published: September 1999
    • format: Paperback
    • isbn: 9780898714364
    • length: 82 pages
    • dimensions: 252 x 176 x 7 mm
    • weight: 0.172kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    Preface
    1. Hyperbolic conservation laws
    Preliminaries
    Riemann problem
    Wave interactions
    Random choice method
    Nonlinear superposition
    Large-time behavior and tegularity
    2. Viscous vonservation laws
    Preliminaries
    Burgers equation
    Diffusion waves
    Viscous shocks
    Viscous rarefaction waves
    Concluding remarks
    Bibliography
    Index.

  • Author

    Tai-Ping Liu, Stanford University, California

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