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

Moon-Jin Kang

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arXiv · 1901.02969

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

Moon-Jin Kang

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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.

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Moon-Jin Kang. 2019-01-09. $L^2$-type contraction for shocks of scalar viscous conservation laws with strictly convex flux. https://arxiv.org/abs/1901.02969

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