Abstract
Here we consider the scalar convex conservation laws in one space dimension with strictly convex flux which is in C 1 . Existence, uniqueness and L 1 contractivity were proved by Kružkov [14] . Using the relative entropy method, Leger showed that for a uniformly convex flux and for the shock wave solutions, the L 2 norm of a perturbed solution relative to the shock wave is bounded by the L 2 norm of the initial perturbation. Here we generalize the result to L p norm for all 1 ⩽ p < ∞ . Also we show that for the non-shock wave solution, L p norm of the perturbed solution relative to the modified N -wave is bounded by the L p norm of the initial perturbation for all 1 ⩽ p < ∞ .
Published Version
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