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

Mohammadreza Raoofi·Kevin Zumbrun
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Abstract

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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Mohammadreza Raoofi, Kevin Zumbrun. 2007-02-14. Stability of undercompressive viscous shock profiles of hyperbolic--parabolic systems. https://arxiv.org/abs/math/0702429

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