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

Margarita Arias; Juan Campos; Cristina Marcelli

doi:10.3934/dcdsb.2009.11.11

Article Contents

2009, Volume 11, Issue 1: 11-30. Doi: 10.3934/dcdsb.2009.11.11

This issue Previous Article Variational models for incompressible Euler equations Next Article A nonlinear interpolation result with application to the summability of minima of some integral functionals

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

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

Received: November 30, 2007

Revised: March 31, 2008

Published: June 2009

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Abstract

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 ($D(0)=0)$.

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

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