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

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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

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

Abstract
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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 & Continuous Dynamical Systems - A, 2008, 20 (4) : 1123-1139. doi: 10.3934/dcds.2008.20.1123

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