Local stability of travelling fronts for a damped wave equation
In: Acta Mathematica Scientia, Jg. 33 (2013), S. 75-83
Online
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Zugriff:
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.
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Local stability of travelling fronts for a damped wave equation
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Autor/in / Beteiligte Person: | Luo, Cao |
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Zeitschrift: | Acta Mathematica Scientia, Jg. 33 (2013), S. 75-83 |
Veröffentlichung: | Elsevier BV, 2013 |
Medientyp: | unknown |
ISSN: | 0252-9602 (print) |
DOI: | 10.1016/s0252-9602(12)60195-7 |
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