English

Propagation properties of reaction-diffusion equations in periodic domains

Analysis of PDEs 2020-12-30 v1

Abstract

This paper studies the phenomenon of invasion for heterogeneous reaction-diffusion equations in periodic domains with monostable and combustion reaction terms. We give an answer to a question rised by Berestycki, Hamel and Nadirashvili in [5] concerning the connection between the speed of invasion and the speed of fronts. To do so, we extend the classical Freidlin-Gartner formula to such equations, using a geometrical argument devised by Rossi in [17], and derive some bounds on the speed of fronts using estimates on the heat kernel.

Keywords

Cite

@article{arxiv.1709.07197,
  title  = {Propagation properties of reaction-diffusion equations in periodic domains},
  author = {Romain Ducasse},
  journal= {arXiv preprint arXiv:1709.07197},
  year   = {2020}
}