Stability of fronts and transient behaviour in KPP systems

Document Type

Conference Proceeding

Publication Date

6-8-2010

Abstract

We consider a system of two reaction diffusion equations with the Kolmogorov-Petrovsky-Piskunov (KPP) type nonlinearity which describes propagation of pressuredriven flames. It is known that the system admits a family of travelling wave solutions parameterized by their velocity. In this paper, we show that these travelling fronts are stable under the assumption that perturbations belong to an appropriate weighted L2 space. We also discuss an interesting meta-stable pattern the system exhibits in certain cases. © 2010 The Royal Society.

Identifier

77953373811 (Scopus)

Publication Title

Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

External Full Text Location

https://doi.org/10.1098/rspa.2009.0400

e-ISSN

14712946

ISSN

13645021

First Page

1769

Last Page

1788

Issue

2118

Volume

466

Grant

0908009

Fund Ref

National Science Foundation

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