Freidlin–Gärtner formula and asymptotic profile in reaction-diffusion equations
Abstract
We address the question of the large-time behavior of solutions to reaction-diffusion equations in periodic media. We start with the description of the asymptotic shape of the invasion set, which is characterized by the Freidlin–Gärtner formula. We outline a proof of the formula that holds true for general types of reaction terms. We then present some recent results, obtained in collaboration with H. Guo and F. Hamel, for (weakly) bistable equations. They include a regular version of the Freidlin–Gärtner formula and the convergence in profile towards pulsating traveling fronts for solutions with either bounded or unbounded initial support.
Fields of Study & Subjects
Mathematical and Theoretical Epidemiology and Ecology Models
Advanced Mathematical Modeling in Engineering
Nonlinear Dynamics and Pattern Formation
Publication details
- Journal / source
- Journées Équations aux dérivées partielles
- Publisher
- MathDoc/Centre Mersenne
- Pages
- 1–12
- Publication date
- 19 June 2026
- Language
- EN