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

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

2010-03-16

arxiv.org/abs/1003.3130v3

Mathematics

Analysis of PDEs

36 pages; this is a final revision, accepted for publication in JDE

Scientific paper

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.

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