  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
$L^1\cap H^2$ 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.
