Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4610477 | Journal of Differential Equations | 2014 | 22 Pages |
Abstract
Here we consider the scalar convex conservation laws in one space dimension with strictly convex flux which is in C1C1. Existence, uniqueness and L1L1 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 L2L2 norm of a perturbed solution relative to the shock wave is bounded by the L2L2 norm of the initial perturbation. Here we generalize the result to LpLp norm for all 1⩽p<∞1⩽p<∞. Also we show that for the non-shock wave solution, LpLp norm of the perturbed solution relative to the modified N -wave is bounded by the LpLp norm of the initial perturbation for all 1⩽p<∞1⩽p<∞.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Adimurthi, Shyam Sundar Ghoshal, G.D. Veerappa Gowda,