Stability of undercompressive viscous shock profiles of hyperbolic--parabolic systems

Details Stability of undercompressive viscous shock profiles of hyperbolic--parabolic systems Stability of undercompressive viscous shock profiles of hyperbolic--parabolic systems

2007-02-14

arxiv.org/abs/math/0702429v1

Mathematics

Analysis of PDEs

37 pp

Scientific paper

Extending to systems of hyperbolic--parabolic conservation laws results of Howard and Zumbrun for strictly parabolic systems, we show for viscous shock profiles of arbitrary amplitude and type that necessary spectral (Evans function) conditions for linearized stability established by Mascia and Zumbrun are also sufficient for linearized and nonlinear phase-asymptotic stability, yielding detailed pointwise estimates and sharp rates of convergence in $L^p$, $1\le p\le \infty$.

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