477 research outputs found
Conditional stability of unstable viscous shocks
Continuing 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
perturbatoins, converging time-asymptotically to a translate of
the unperturbed wave. That is, for a shock with unstable eigenvalues, we
establish conditional stability on a codimension- manifold of initial data,
with sharp rates of decay in all . For , we recover the result of
unconditional stability obtained by Howard, Mascia, and Zumbrun
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