English

Transition fronts and stretching phenomena for a general class of reaction-dispersion equations

Analysis of PDEs 2015-06-11 v1

Abstract

We consider a general form of reaction-dispersion equations with non-local dispersal and local reaction. Under some general conditions, we prove the non-existence of transition fronts, as well as some stretching properties at large time for the solutions of the Cauchy problem. These conditions are satisfied in particular when the reaction is monostable and when the dispersal operator is either the fractional Laplacian, a convolution operator with a fat-tailed kernel or a nonlinear fast diffusion operator.

Keywords

Cite

@article{arxiv.1506.03315,
  title  = {Transition fronts and stretching phenomena for a general class of reaction-dispersion equations},
  author = {Jimmy Garnier and François Hamel and Lionel Roques},
  journal= {arXiv preprint arXiv:1506.03315},
  year   = {2015}
}