Stability of Steady Solutions of Burgers's Equation

We develop tools to discuss the stability of viscous shock profiles for conservation laws. The technique is based on replacing the far field regions by boundary conditions that describe the effect of the outer solution on the solution in the shock layer region. We apply the technique to Burgers'...

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Bibliographic Details
Published inSIAM journal on numerical analysis Vol. 35; no. 6; pp. 2329 - 2349
Main Authors Kreiss, Gunilla, Kreiss, Heinz-Otto
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.12.1998
Subjects
Boundary conditions
Boundary value problems
Conservation laws
Continuous spectra
Eigenvalues
Estimates
Exact sciences and technology
Laplace transformation
Laplace transforms
Mathematical analysis
Mathematical theorems
Mathematics
Nonlinearity
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Scalars
Sciences and techniques of general use
Shock layer
Parabolic equation
Parseval relation
Differential equation
Initial value problem
Eigenvalue problem
Laplace transformation
Sobolev inequality
Viscous shock profile
Partial differential equation
Non linear stability
Burger equation
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Summary:We develop tools to discuss the stability of viscous shock profiles for conservation laws. The technique is based on replacing the far field regions by boundary conditions that describe the effect of the outer solution on the solution in the shock layer region. We apply the technique to Burgers's equation and prove stability for perturbations that are not localized in space.
ISSN:0036-1429
1095-7170
DOI:10.1137/S0036142997316001