Advances in Differential Equations

Front propagation in bistable reaction-diffusion-advection equations

Luisa Malaguti, Cristina Marcelli, and Serena Matucci

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Abstract

The paper deals with the existence and properties of front propagation between the stationary states $0$ and $1$ of the reaction-diffusion-advection equation $$ v_\tau + h(v)v_x = \big( D(v) v_x \big)_x + G(v), $$ where $G$ is a bistable reaction term and $D$ is a strictly positive diffusive process. We show that the additional transport term $h$ can cause the disappearance of such wavefronts and prove that their existence depends both on the local behavior of $G$ and $h$ near the unstable equilibrium and on a suitable sign condition on $h$ in $[0,1]$. We also provide an estimate of the wave speed, which can be negative even if $\int_0^1 G(u) D(u) du>0$, unlike what happens to the mere reaction-diffusion dynamic occurring when $h\equiv 0$.

Article information

Source
Adv. Differential Equations Volume 9, Number 9-10 (2004), 1143-1166.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867916

Mathematical Reviews number (MathSciNet)
MR2098068

Zentralblatt MATH identifier
1101.35009

Subjects
Primary: 35K57: Reaction-diffusion equations
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 92D25: Population dynamics (general)

Citation

Malaguti, Luisa; Marcelli, Cristina; Matucci, Serena. Front propagation in bistable reaction-diffusion-advection equations. Adv. Differential Equations 9 (2004), no. 9-10, 1143--1166. https://projecteuclid.org/euclid.ade/1355867916.


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