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arXiv · 1911.12526

L^2-type contraction of viscous shocks for large family of scalar conservation laws

Logan Stokols
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Abstract

In this paper we study small shocks of 1D scalar viscous conservation laws with uniformly convex flux and nonlinear dissipation. We show that such shocks are L2 stable independent of the strength of the dissipation, even with large perturbations. The proof uses the relative entropy method with a spatially-inhomogeneous psuedo-norm.

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Logan Stokols. 2019-11-28. L^2-type contraction of viscous shocks for large family of scalar conservation laws. https://arxiv.org/abs/1911.12526

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