Conditional stability of unstable viscous shocks

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dc.creatorZumbrun, Kevin
dc.date2008-11-07
dc.date.accessioned2026-07-07T10:16:52Z
dc.date.available2026-07-07T10:16:52Z
dc.descriptionContinuing a line of investigation initiated by Texier and Zumbrun on dynamics of viscous shock and detonation waves, we show that a linearly unstable Lax-type viscous shock solution of a semilinear strictly parabolic system of conservation laws possesses a translation-invariant center stable manifold within which it is nonlinearly orbitally stable with respect to small $L^1\cap H^2$ perturbatoins, converging time-asymptotically to a translate of the unperturbed wave. That is, for a shock with $p$ unstable eigenvalues, we establish conditional stability on a codimension-$p$ manifold of initial data, with sharp rates of decay in all $L^p$. For $p=0$, we recover the result of unconditional stability obtained by Howard, Mascia, and Zumbrun.
dc.identifierhttps://arxiv.org/abs/0811.1193
dc.identifierhttp://arxiv.org/abs/0811.1193
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173662
dc.subjectAnalysis of PDEs
dc.subject35B35
dc.titleConditional stability of unstable viscous shocks
dc.typetext

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