Acta mathematica scientia, Series B >
LOCAL STABILITY OF TRAVELLING FRONTS FOR A DAMPED WAVE EQUATION
Received date: 2012-01-14
Revised date: 2012-03-28
Online published: 2013-01-20
The paper is concerned with the long-time behaviour of the travelling fronts of the damped wave equation ∂utt+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.
Key words： travelling front; local stability; damped wave equation
LUO Cao . LOCAL STABILITY OF TRAVELLING FRONTS FOR A DAMPED WAVE EQUATION[J]. Acta mathematica scientia, Series B, 2013 , 33(1) : 75 -83 . DOI: 10.1016/S0252-9602(12)60195-7
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