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2007 Nonlinear stability of degenerate shock profiles
Peter Howard
Differential Integral Equations 20(5): 515-560 (2007). DOI: 10.57262/die/1356039442


We consider degenerate viscous shock profiles arising in systems of two regularized conservation laws, where degeneracy here describes viscous shock profiles for which the asymptotic endstates are sonic to the associated hyperbolic system (the shock speed is equal to one of the characteristic speeds). Proceeding with pointwise estimates on the Green's function for the linear system of equations that arises upon linearization of the conservation law about a degenerate viscous shock profile, we establish that spectral stability, defined in terms of an Evans function, implies nonlinear stability. The asymptotic rate of decay for the perturbation is found both pointwise and in all $L^p$ norms, $p \ge 1$.


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Peter Howard. "Nonlinear stability of degenerate shock profiles." Differential Integral Equations 20 (5) 515 - 560, 2007.


Published: 2007
First available in Project Euclid: 20 December 2012

zbMATH: 1212.35298
MathSciNet: MR2324219
Digital Object Identifier: 10.57262/die/1356039442

Primary: 35L65
Secondary: 35B35 , 35B40 , 35K55 , 35L67

Rights: Copyright © 2007 Khayyam Publishing, Inc.

Vol.20 • No. 5 • 2007
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