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We consider scalar nonviscous conservation laws with strictly convex flux inone spatial dimension, and we investigate the behavior of bounded L^2perturbations of shock wave solutions to the Riemann problem using the relativeentropy 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 boundedabove by the L^2 norm of the initial perturbation.

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