On existence of semi-wavefronts for a non-local reaction-diffusion equation with distributed delay

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:463

Article

Aguerrea, Maitere¹  Gomez, Carlos¹ 

[1] Univ Catolica Maule, Fac Ciencias Basicas, Casilla 617, Talca, Chile

关键词: Reaction-diffusion equation;    Traveling wave;    Non-local interaction;    Delay;    Existence;   

DOI  :  10.1016/j.jmaa.2018.03.042

来源: Elsevier

【 摘 要 】

We study the problem of existence of semi-wavefront solutions for a non-local delayed reaction-diffusion equation with monostable nonlinearity. In difference with previous works, we consider non-local interaction which can be asymmetric in space. As a consequence of this asymmetry, we must analyze the existence of expansion waves for both positive and negative speeds. In the paper, we use a framework of the general theory recently developed for a certain nonlinear convolution equation. This approach allows us to prove the wave existence for the range of admissible speeds c is an element of R \ (c(*)(-), c(*)(+)), where the critical speeds c(*)(-) and et can c(*)(+) calculated explicitly from some associated equations. The main result is then applied to several non-local reaction-diffusion epidemic and population models. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free