LP-decay rates for perturbations of degenerate scalar viscous shock waves

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:382

Article

Plaza, Ramon G.

关键词: Viscous degenerate shocks;    L-p-decay rates;    Energy estimates;   

DOI  :  10.1016/j.jmaa.2011.04.091

来源: Elsevier

【 摘 要 】

This contribution shows how to obtain L-p-decay rates, with 2 <= p <= +infinity, for zero-mass perturbations of degenerate scalar viscous shock waves using energy methods. The proof is based upon previous work by Matsumura and Nishihara (Comm. Math. Phys. 165 (1) (1994) 83-96), by extending their weighted energy estimates to L-p-norms, and by obtaining sharp decay rates for the antiderivative of the perturbation with the aid of basic interpolation inequalities. The analysis applies to shocks of all orders of degeneracy and it is elementary. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free