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Large Time Behavior of Solutions for General Quasilinear Hyperbolic-Parabolic Systems of Conservation Laws
Tai-Ping Liu, Stanford University, CA, and Yanni Zeng, State University of New York at Stony Brook, NY

Memoirs of the American Mathematical Society
1997; 120 pp; softcover
Volume: 125
ISBN-10: 0-8218-0545-2
ISBN-13: 978-0-8218-0545-9
List Price: US$48
Individual Members: US$28.80
Institutional Members: US$38.40
Order Code: MEMO/125/599
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Physical models of conservation form--such as the compressible Navier-Stokes equations, and MHD and full nonlinear elasticity equations--are not uniformly parabolic, but rather hyperbolic-parabolic. This memoir gives a self-contained analysis of nonlinear interactions of dissipation waves as well as the hyperbolic aspects of general systems. It introduces the new pointwise estimates of Green functions and coupling of nonlinear waves.


Graduate students and research mathematicians interested in partial differential equations.

Table of Contents

  • Introduction
  • Viscous conservation laws
  • Diffusion waves
  • Systems with diagonalizable linearizations
  • Green's function for a \(2\times 2\) linear system
  • Green's functions for \(n\times n\) systems with applications
  • Energy estimate
  • Systems with non-diagonalizable linearizations
  • Applications to continuum mechanics
  • References
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