Topological Methods in Nonlinear Analysis

Traveling front solutions in nonlinear diffusion degenerate Fisher-KPP and Nagumo equations via the Conley index

Fatiha El Adnani and Hamad Talibi Alaoui

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Abstract

Existence of one dimensional traveling wave solutions $u( x,t):=\phi ( x-ct) $ at the stationary equilibria, for the nonlinear degenerate reaction-diffusion equation $u_{t}=[K( u)u_{x}]_{x}+F( u) $ is studied, where $K$ is the density coefficient and $F$ is the reactive part. We use the Conley index theory to show that there is a traveling front solutions connecting the critical points of the reaction-diffusion equations. We consider the nonlinear degenerate generalized Fisher-KPP and Nagumo equations.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 35, Number 1 (2010), 43-60.

Dates
First available in Project Euclid: 21 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1461249000

Mathematical Reviews number (MathSciNet)
MR2677429

Zentralblatt MATH identifier
1213.35168

Citation

El Adnani, Fatiha; Alaoui, Hamad Talibi. Traveling front solutions in nonlinear diffusion degenerate Fisher-KPP and Nagumo equations via the Conley index. Topol. Methods Nonlinear Anal. 35 (2010), no. 1, 43--60. https://projecteuclid.org/euclid.tmna/1461249000


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