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July  2008, 10(1): 149-170. doi: 10.3934/dcdsb.2008.10.149

Stability of travelling waves with noncritical speeds for double degenerate Fisher-Type equations

Yi Li 1, and  Yaping Wu 2,

1. 

Department of Mathematics, University of Iowa, Iowa, IA 52242, United States
2. 

Department of Mathematics, Capital Normal University, Beijing 100037

Received  May 2007 Revised  March 2008 Published  April 2008

This paper is concerned with the asymptotic stability of travel- ling wave solutions for double degenerate Fisher-type equations. By spectral analysis, each travelling front solution with non-critical speed is proved to be linearly exponentially stable in some exponentially weighted spaces. Further by Evans function method and detailed semigroup estimates each travelling front solution with non-critical speed is proved to be locally algebraically stable to perturbations in some polynomially weighted spaces, and it is also locally exponentially stable to perturbations in some polynomially and exponentially weighted spaces.
Keywords: asymptotic stability, semigroup estimates, travelling waves, algebraic decay, Evans function., spectral analysis.
Mathematics Subject Classification: Primary: 35B35, 35K57, Secondary: 35A18, 35B4.
Citation: Yi Li, Yaping Wu. Stability of travelling waves with noncritical speeds for double degenerate Fisher-Type equations. Discrete & Continuous Dynamical Systems - B, 2008, 10 (1) : 149-170. doi: 10.3934/dcdsb.2008.10.149
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