Differential and Integral Equations

A variational proof of global stability for bistable travelling waves

Thierry Gallay and Emmanuel Risler

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Abstract

We give a variational proof of global stability for bistable travelling waves of scalar reaction-diffusion equations on the real line. In particular, we recover some of the classical results by P.~Fife and J.B.~McLeod (1977) without any use of the maximum principle. The method that is illustrated here in the simplest possible setting has been successfully applied to more general parabolic or hyperbolic gradient-like systems.

Article information

Source
Differential Integral Equations, Volume 20, Number 8 (2007), 901-926.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356039363

Mathematical Reviews number (MathSciNet)
MR2339843

Zentralblatt MATH identifier
1212.35210

Subjects
Primary: 35K57: Reaction-diffusion equations
Secondary: 34D23: Global stability 35A15: Variational methods 35B35: Stability 35Q51: Soliton-like equations [See also 37K40] 47J30: Variational methods [See also 58Exx]

Citation

Gallay, Thierry; Risler, Emmanuel. A variational proof of global stability for bistable travelling waves. Differential Integral Equations 20 (2007), no. 8, 901--926. https://projecteuclid.org/euclid.die/1356039363


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