Differential and Integral Equations

Propagating interface in a monostable reaction-diffusion equation with time delay

Matthieu Alfaro and Arnaud Ducrot

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Abstract

We consider a monostable time-delayed reaction-diffusion equation arising from population dynamics models. We let a small parameter tend to zero and investigate the behavior of the solutions. We construct accurate lower barriers---by using a nonstandard bistable approximation of the monostable problem---and upper barriers. As a consequence, we prove the convergence to a propagating interface.

Article information

Source
Differential Integral Equations, Volume 27, Number 1/2 (2014), 81-104.

Dates
First available in Project Euclid: 12 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1384282855

Mathematical Reviews number (MathSciNet)
MR3161597

Zentralblatt MATH identifier
1313.35160

Subjects
Primary: 35K57: Reaction-diffusion equations 35R10: Partial functional-differential equations 92D25: Population dynamics (general)

Citation

Alfaro, Matthieu; Ducrot, Arnaud. Propagating interface in a monostable reaction-diffusion equation with time delay. Differential Integral Equations 27 (2014), no. 1/2, 81--104. https://projecteuclid.org/euclid.die/1384282855


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