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Sharp pointwise bounds for perturbed viscous shock waves
Peter Howard, Mohammadreza Raoofi, Kevin Zumbrun
Refining previous work in \cite{Z.3, MaZ.3, Ra, HZ, HR}, we derive sharp pointwise bounds on behavior of perturbed viscous shock profiles for large-amplitude Lax or overcompressive…
Uniform stability estimates for constant-coefficient symmetric hyperbolic boundary value problems
Olivier Gues, Guy Metivier, Mark Williams +1
Answering a question left open in \cite{MZ2}, we show for general symmetric hyperbolic boundary problems with constant coefficients, including in particular systems with characteri…
Stability of undercompressive shock profiles
Peter Howard, Kevin Zumbrun
Using a simplified pointwise iteration scheme, we establish nonlinear phase-asymptotic orbital stability of large-amplitude Lax, undercompressive, overcompressive, and mixed under-…
Hyperbolic Boundary Value Problems for Symmetric Systems with Variable Multiplicities
Guy Métivier, Kevin Zumbrun
We extend the Kreiss--Majda theory of stability of hyperbolic initial--boundary-value and shock problems to a class of systems, notably including the equations of magnetohydrodynam…
Planar stability critera for viscous shock waves of systems with real viscosity
Kevin Zumbrun
We present a streamlined account of recent developments in the stability theory for planar viscous shock waves, with an emphasis on applications to physical models with ``real,'' o…
Symmetrizers and Continuity of Stable Subspaces for Parabolic-Hyperbolic Boundary Value Problems
Guy Metivier, Kevin Zumbrun
In this paper we prove the continuity of stable subspaces associated to parabolic-hyperbolic boundary value problems, for limiting values of parameters. The analysis is based on th…