Smooth solutions and singularity formation for the inhomogeneous nonlinear wave equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:252

Article

Chen, Geng²  Young, Robin¹ 

[1] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA

[2] Penn State Univ, Dept Math, University Pk, PA 16802 USA

关键词: Wave equation;    Conservation laws;    Shock formation;    Nonlinear elasticity;    Compressible Euler equations;   

DOI  :  10.1016/j.jde.2011.09.004

来源: Elsevier

【 摘 要 】

We study the nonlinear inhomogeneous wave equation in one space dimension: nu(tt) - T (nu, x)(xx) = 0. By constructing some de coupled Riccati type equations for smooth solutions, we provide a singularity formation result without restrictions on the total variation of the data, which generalizes earlier singularity results of Lax and the first author. We apply these results to compressible Euler flows with a general pressure law and elasticity in an inhomogeneous medium. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free