Stability of traveling waves with critical speeds for $P$-degree Fisher-type equations

Yaping Wu; Xiuxia Xing

doi:10.3934/dcds.2008.20.1123

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2008, Volume 20, Issue 4: 1123-1139. Doi: 10.3934/dcds.2008.20.1123

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Stability of traveling waves with critical speeds for $P$-degree Fisher-type equations

Yaping Wu^1, and
Xiuxia Xing^2,

1.
Department of Mathematics, Capital Normal University, Beijing 100037
2.
College of Applied Science, Beijing University of Technology, Beijing 100022

Received: December 31, 2006

Revised: September 30, 2007

Published: September 2008

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Abstract

This paper is concerned with the stability of the traveling front solutions with critical speeds for a class of $p$-degree Fisher-type equations. By detailed spectral analysis and sub-supper solution method, we first show that the traveling front solutions with critical speeds are globally exponentially stable in some exponentially weighted spaces. Furthermore by Evans's function method, appropriate space decomposition and detailed semigroup decaying estimates, we can prove that the waves with critical speeds are locally asymptotically stable in some polynomially weighted spaces, which verifies some asymptotic phenomena obtained by numerical simulations.

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Mathematics Subject Classification: Primary: 35B35, 35A18; Secondary: 35K57, 35B40.

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