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

Fatiha El Adnani, Hamad Talibi Alaoui

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.

Keywords


Traveling front; degenerate nonlinear diffusion; Conley index; connected simple systems

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