Optimal Estimates on the Propagation of Reactions with Fractional Diffusion

Yuming Paul Zhang; Andrej Zlatos

Optimal Estimates on the Propagation of Reactions with Fractional Diffusion

Analysis of PDEs 2023-08-01 v3

Authors: Yuming Paul Zhang , Andrej Zlatos

Abstract

We study the reaction-fractional-diffusion equation $u_t+(-\Delta)^{s} u=f(u)$ with ignition and monostable reactions $f$ , and $s\in(0,1)$ . We obtain the first optimal bounds on the propagation of front-like solutions in the cases where no traveling fronts exist. Our results cover most of these cases, and also apply to propagation from localized initial data.

Keywords

reaction-fractional-diffusion equation ignition reaction monostable reaction front propagation optimal bounds localized initial data

Cite

@article{arxiv.2105.12800,
  title  = {Optimal Estimates on the Propagation of Reactions with Fractional Diffusion},
  author = {Yuming Paul Zhang and Andrej Zlatos},
  journal= {arXiv preprint arXiv:2105.12800},
  year   = {2023}
}

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