$L^2$-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 related 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 [18] 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.

References in corpus (1)

• $L^2$-contraction of large planar shock waves for multi-dimensional scalar viscous conservation laws

Cited by in corpus (4)

• Uniqueness of a planar contact discontinuity for 3D compressible Euler system in a class of zero dissipation limits from Navier-Stokes-Fourier system
• Time-asymptotic stability of composite waves of viscous shock and rarefaction for barotropic Navier-Stokes equations
• Uniqueness and stability of entropy shocks to the isentropic Euler system in a class of inviscid limits from a large family of Navier-Stokes systems
• L^2-type contraction of viscous shocks for large family of scalar conservation laws