Fastness and continuous dependence in front propagation in Fisher-KPP equations

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January 2009, 11(1): 11-30. doi: 10.3934/dcdsb.2009.11.11

Fastness and continuous dependence in front propagation in Fisher-KPP equations

Margarita Arias ^1, , Juan Campos ^1, and Cristina Marcelli ^2,

1.	Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain
2.	Dipartimento di Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche, 60131 Ancona, Italy

Received December 2007 Revised April 2008 Published November 2008

Abstract
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We investigate the continuous dependence of the minimal speed of propagation and the profile of the corresponding travelling wave solution of Fisher-type reaction-diffusion equations

$\vartheta_t = (D(\vartheta)\vartheta_x)_x + f(\vartheta)$

with respect to both the reaction term $f$ and the diffusivity $D$.
We also introduce and discuss the concept of fast heteroclinic in this context, which allows to interpret the appearance of sharp heteroclinic in the case of degenerate diffusivity ($D(0)=0)$.

Keywords: travelling wave solutions, continuous dependence, degenerate diffusivity, fast heteroclinic, sharp solutions, reaction-diffusion equations, wave speed.

Mathematics Subject Classification: Primary: 35K57, 58F17; Secondary: 34B40.

Citation: Margarita Arias, Juan Campos, Cristina Marcelli. Fastness and continuous dependence in front propagation in Fisher-KPP equations. Discrete & Continuous Dynamical Systems - B, 2009, 11 (1) : 11-30. doi: 10.3934/dcdsb.2009.11.11

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