Adimurthi, . ; Ghoshal, Shyam Sundar ; Veerappa Gowda, G.D. (2014) Lp stability for entropy solutions of scalar conservation laws with strict convex flux Journal of Differential Equations, 256 (10). pp. 3395-3416. ISSN 0022-0396
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Official URL: http://doi.org/10.1016/j.jde.2014.02.005
Related URL: http://dx.doi.org/10.1016/j.jde.2014.02.005
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<∞.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier Science. |
| Keywords: | Hamilton-Jacobi Equation; Scalar Conservation Laws; Characteristic Lines; Asymptotically Single Shock Packet. |
| ID Code: | 119742 |
| Deposited On: | 16 Jun 2021 13:35 |
| Last Modified: | 16 Jun 2021 13:35 |
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