Freidlin-Gärtner formula and asymptotic profile in reaction-diffusion equations

Fuente: arXiv
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Main Author: Rossi, Luca
Format: Preprint
Published: 2026
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author Rossi, Luca
author_facet Rossi, Luca
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2604_27556
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Freidlin-Gärtner formula and asymptotic profile in reaction-diffusion equations
Rossi, Luca
Analysis of PDEs
35B30, 35B40, 35C07, 35K57
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.
title Freidlin-Gärtner formula and asymptotic profile in reaction-diffusion equations
topic Analysis of PDEs
35B30, 35B40, 35C07, 35K57
url https://arxiv.org/abs/2604.27556