Lp stability for entropy solutions of scalar conservation laws with strict convex flux

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:256

Article

Adimurthi¹  Ghoshal, Shyam Sundar²  Gowda, G. D. Veerappa¹ 

[1] Tata Inst Fundamental Res, Ctr Applicable Math, Bangalore, Karnataka, India

[2] Univ Franche Comte, Math Lab, F-25030 Besancon, France

关键词: Hamilton-Jacobi equation;    Scalar conservation laws;    Characteristic lines;    Asymptotically single shock packet;   

DOI  :  10.1016/j.jde.2014.02.005

来源: Elsevier

【 摘 要 】

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 Kruzkov [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 < infinity. 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 < infinity. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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