LOCAL STABILITY OF TRAVELLING FRONTS FOR A DAMPED WAVE EQUATION

The paper is concerned with the long-time behaviour of the travelling fronts of the damped wave equation αutt ＋ut = uxx -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 ut = uxx - V′（u）. Whereas a lot...

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Bibliographic Details
Published inActa mathematica scientia Vol. 33; no. 1; pp. 75 - 83
Main Author 罗操
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 2013
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
Subjects
35B35
35B40
37L15
37L70
Asymptotic properties
Combustion
damped wave equation
local stability
Mathematical analysis
Nonlinearity
Reaction-diffusion equations
Stability
travelling front
Wave equations
乘车
单稳态
双曲型方程组
局部稳定性
扩散方程
抛物系统
阵地
阻尼波动方程
local stability
37L15
travelling front
35B35
damped wave equation
37L70
35B40
Online AccessGet full text
ISSN0252-9602
1572-9087
DOI10.1016/S0252-9602(12)60195-7

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Summary:The paper is concerned with the long-time behaviour of the travelling fronts of the damped wave equation αutt ＋ut = uxx -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 ut = uxx - 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.
Bibliography:travelling front; local stability; damped wave equation
The paper is concerned with the long-time behaviour of the travelling fronts of the damped wave equation αutt ＋ut = uxx -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 ut = uxx - 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.
42-1227/O
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SourceType-Scholarly Journals-1
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content type line 23
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(12)60195-7