L-2-type contraction for shocks of scalar viscous conservation laws with strictly convex flux

Abstract

We study the L-2-type contraction property of large perturbations around shock waves of scalar viscous conservation laws with strictly convex fluxes in one space dimension. The contraction holds up to a shift, and it is measured by a weighted relative entropy, for which we choose an appropriate entropy associated with the strictly convex flux. In particular, we handle shocks with small amplitude. This result improves the recent article [19] of the author and Vasseur on L-2-contraction property of shocks to scalar viscous conservation laws with a special flux, that is almost the Burgers flux.