Differential and Integral Equations
- Differential Integral Equations
- Volume 20, Number 8 (2007), 901-926.
A variational proof of global stability for bistable travelling waves
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.
Differential Integral Equations, Volume 20, Number 8 (2007), 901-926.
First available in Project Euclid: 20 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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