Multi-dimensional stability of planar Lax shocks in hyperbolic-elliptic coupled systems

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Abstract

We study nonlinear time-asymptotic stability of small-amplitude planar Lax shocks in a model consisting of a system of multi-dimensional conservation laws coupled with an elliptic system. Such a model can be found in context of dynamics of a gas in presence of radiation. Our main result asserts that the standard uniform Evans stability condition implies nonlinear stability. The main analysis is based on the earlier developments by Zumbrun for multi-dimensional viscous shock waves and by Lattanzio-Mascia-Nguyen-Plaza-Zumbrun for one-dimensional radiative shock profiles.

Original languageEnglish (US)
Pages (from-to)382-411
Number of pages30
JournalJournal of Differential Equations
Volume252
Issue number1
DOIs
StatePublished - Jan 1 2012

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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