Admissable wavefront speeds for a single species reaction-diffusion equation with delay. (English) Zbl 1154.34032

Trofimchuk, Elena; Trofimchuk, Sergei

Discrete Contin. Dyn. Syst. 20, No. 2, 407-423 (2008).

In this article the existence of positive and generally nonmonotone travelling waves of a family of delayed reaction-diffusion equations with exactly two non-negative equilibria is studied. Important examples of such an equation are the Nicholson’s blowflies and the Mackey-Glass equation. By using suitable fixed-point theorems, the authors establish the existence of not necessarily monotone travelling fronts while obtaining sharp lower bounds for the travelling wave speed. Moreover, the authors also obtain quite general results for the possibly compact set of admissable wave speeds.

Reviewer: Marc Georgi (Berlin)

MSC:

34K10	Boundary value problems for functional-differential equations
35R10	Functional partial differential equations
34E05	Asymptotic expansions of solutions to ordinary differential equations

Keywords:

time-delayed reaction diffusion equation; heteroclinic solutions; non-monotone positive travelling fronts; single species population models