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July  1999, 5(3): 473-488. doi: 10.3934/dcds.1999.5.473

A singular perturbed problem for semilinear wave equations with small parameter

Han Yang 1,

1. 

Institute of Applied Mathematics, South-west Jiaotong University, Chengdu 610031, China

Received  November 1998 Revised  May 1999 Published  May 1999

In this paper we get a lower bound independent of $\delta$ on the life-span of classical solutions to the following Cauchy problem by using the global iteration method

$\delta u_{t t}-\Delta u +u_t = F(u, \nabla u),$

$t = 0 : u = \epsilon u_0(x), u_t = \epsilon u_1(x),$

where $\delta$ and $\epsilon$ are small positive parameters. Moreover, we consider the related singular perturbated problem as $\delta\to 0$ and show that the perturbated term $\delta u_{t t}$ has an appreciable effect only for a short times.

Keywords: singular perturbation., Cauchy problem, life-span of classical solutions.
Mathematics Subject Classification: 35b25, 35l2.
Citation: Han Yang. A singular perturbed problem for semilinear wave equations with small parameter. Discrete & Continuous Dynamical Systems, 1999, 5 (3) : 473-488. doi: 10.3934/dcds.1999.5.473
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