L^2 stability estimates for shock solutions of scalar conservation laws using the relative entropy method

Details L^2 stability estimates for shock solutions of scalar conservation laws using the relative entropy method L^2 stability estimates for shock solutions of scalar conservation laws using the relative entropy method

2009-11-20

arxiv.org/abs/0911.3940v1

Mathematics

Analysis of PDEs

17 pages

Scientific paper

We consider scalar nonviscous conservation laws with strictly convex flux in one spatial dimension, and we investigate the behavior of bounded L^2 perturbations of shock wave solutions to the Riemann problem using the relative entropy method. We show that up to a time-dependent translation of the shock, the L^2 norm of a perturbed solution relative to the shock wave is bounded above by the L^2 norm of the initial perturbation.

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