Long-time behavior of solutions to a nonlinear hyperbolic relaxation system

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:228

Article

Orive, Rafael ; Zuazua, Enrique

关键词: hyperbolic relaxation system;    damped wave equations;    convective heat equation;    asymptotic behavior;    blow-up;   

DOI  :  10.1016/j.jde.2006.04.014

来源: Elsevier

【 摘 要 】

We study the large time behavior of solutions of a one-dimensional hyperbolic relaxation system that may be written as a nonlinear damped wave equation. First, we prove the global existence of a unique solution and their decay properties for sufficiently small initial data. We also show that for some large initial data, solutions blow-up in finite time. For quadratic nonlinearities, we prove that the large time behavior of solutions is given by the fundamental solution of the viscous Burgers equation. In some other cases, the convection term is too weak and the large time behavior is given by the linear heat kernel. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

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