LOCAL STABILITY OF TRAVELLING FRONTS FOR A DAMPED WAVE EQUATION

doi:10.1016/S0252-9602(12)60195-7

数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (1): 75-83.doi: 10.1016/S0252-9602(12)60195-7

LOCAL STABILITY OF TRAVELLING FRONTS FOR A DAMPED WAVE EQUATION

罗操

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

收稿日期:2012-01-14 修回日期:2012-03-28 出版日期:2013-01-20 发布日期:2013-01-20

LOCAL STABILITY OF TRAVELLING FRONTS FOR A DAMPED WAVE EQUATION

LUO Cao

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received:2012-01-14 Revised:2012-03-28 Online:2013-01-20 Published:2013-01-20

摘要/Abstract

摘要：

The paper is concerned with the long-time behaviour of the travelling fronts of the damped wave equation ∂u_tt+u_t= u_xx−V ′(u) on R. The long-time asymptotics of the solutions of this equation are quite similar to those of the corresponding reaction-diffusion equation u_t= u_xx − V ′(u). Whereas a lot is known about the local stability of travelling fronts in parabolic systems, for the hyperbolic equations it is only briefly discussed when the potential V is of bistable type. However, for the combustion or monostable type of V , the problem is much more complicated. In this paper, a local stability result for travelling fronts of this equation with combustion type of nonlinearity is established. And then, the result is extended to the damped wave equation with a case of monostable pushed front.

关键词: travelling front, local stability, damped wave equation

Abstract:

Key words: travelling front, local stability, damped wave equation

中图分类号:

35B35

罗操. LOCAL STABILITY OF TRAVELLING FRONTS FOR A DAMPED WAVE EQUATION[J]. 数学物理学报(英文版), 2013, 33(1): 75-83.

LUO Cao. LOCAL STABILITY OF TRAVELLING FRONTS FOR A DAMPED WAVE EQUATION[J]. Acta mathematica scientia,Series B, 2013, 33(1): 75-83.

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LOCAL STABILITY OF TRAVELLING FRONTS FOR A DAMPED WAVE EQUATION

LOCAL STABILITY OF TRAVELLING FRONTS FOR A DAMPED WAVE EQUATION

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