For scalar viscous conservation laws with polynomial flux u^p, p in [2,4], arbitrarily large viscous shock profiles are L2-contractive and time-asymptotically stable under small H1 perturbations, with t^{-1/4} decay for L1 perturbations.
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$L^2$-contraction and asymptotic stability of large shock for scalar viscous conservation laws
For scalar viscous conservation laws with polynomial flux u^p, p in [2,4], arbitrarily large viscous shock profiles are L2-contractive and time-asymptotically stable under small H1 perturbations, with t^{-1/4} decay for L1 perturbations.