Shock waves in conservation laws with physical viscosity

We study the perturbation of a shock wave in conservation laws with physical viscosity. We obtain the detailed pointwise estimates of the solutions. In particular, we show that the solution converges to a translated shock profile. The strength of the perturbation and that of the shock are assumed to...

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Bibliographic Details
Main Authors: Liu, Tai-Ping, Zeng, Yanni
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2015
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
Conservation laws (Mathematics)
Green''s functions
Mathematics
Shock waves
Shock waves > Mathematics
Conservation laws
Green’s function
nonlinear stability
wave interactions
compressible Navier-Stokes equations
magneto-hydrodynamics
physical viscosity
large time behavior
pointwise estimates
quasilinear hyperbolic-parabolic systems
shock waves
ISBN:9781470410162, 1470410168
ISSN:0065-9266, 1947-6221
Online Access:Get full text
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Table of Contents:
  • Introduction -- Preliminaries -- Green’s functions for Systems with Constant Coefficients -- Green’s Function for Systems Linearized Along Shock Profiles -- Estimates on Green’s Function -- Estimates on Crossing of Initial Layer -- Estimates on Truncation Error -- Energy Type Estimates -- Wave Interaction -- Stability Analysis -- Application to Magnetohydrodynamics
  • Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Preliminaries -- Chapter 3. Green's functions for Systems with Constant Coefficients -- Chapter 4. Green's Function for Systems Linearized Along Shock Profiles -- Chapter 5. Estimates on Green's Function -- Chapter 6. Estimates on Crossing of Initial Layer -- Chapter 7. Estimates on Truncation Error -- Chapter 8. Energy Type Estimates -- Chapter 9. Wave Interaction -- Chapter 10. Stability Analysis -- Chapter 11. Application to Magnetohydrodynamics -- References -- Back Cover