Communications in Mathematical Sciences

Volume 16 (2018)

Number 2

Anomalous invasion speed in a system of coupled reaction-diffusion equations

Pages: 441 – 461

DOI: http://dx.doi.org/10.4310/CMS.2018.v16.n2.a7

Authors

Grégory Faye (Institut de Mathématiques de Toulouse, Université de Toulouse, France)

Gwenaël Peltier (Institut de Mathématiques de Toulouse, Université de Toulouse, France)

Abstract

In this paper, we provide a complete description of the selected spreading speed of systems of reaction-diffusion equations with unilateral coupling and prove the existence of anomalous spreading speeds for systems with monostable nonlinearities. Our work extends known results for systems with linear and quadratic couplings, and Fisher-KPP type nonlinearities. Our proofs rely on the construction of appropriate sub- and super-solutions.

Keywords

anomalous spreading speed, linear spreading speed, sub- and super-solutions

2010 Mathematics Subject Classification

35B40, 35B51, 35C07, 35K57

Full Text (PDF format)

Received 26 September 2016

Accepted 1 December 2017

Published 14 May 2018