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October  2008, 20(4): 1123-1139. doi: 10.3934/dcds.2008.20.1123

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  January 2007 Revised  October 2007 Published  January 2008

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.
Keywords: sub-supper solutions, traveling fronts, Evans's function., asymptotic stability, spectral analysis.
Mathematics Subject Classification: Primary: 35B35, 35A18; Secondary: 35K57, 35B4.
Citation: Yaping Wu, Xiuxia Xing. Stability of traveling waves with critical speeds for $P$-degree Fisher-type equations. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 1123-1139. doi: 10.3934/dcds.2008.20.1123
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