Traveling wave solutions of a reaction-diffusion equation with state-dependent delay

Guo Lin; Haiyan  Wang

doi:10.3934/cpaa.2016.15.319

Article Contents

2016, Volume 15, Issue 2: 319-334. Doi: 10.3934/cpaa.2016.15.319

This issue Previous Article On the nonlocal Cahn-Hilliard-Brinkman and Cahn-Hilliard-Hele-Shaw systems Next Article Remarks on weak solutions of fractional elliptic equations

Traveling wave solutions of a reaction-diffusion equation with state-dependent delay

Guo Lin^1, and
Haiyan Wang^2,

1.
School of Mathematics and Statistics, Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou, Gansu 730000
2.
Department of Mathematics, Northwest Normal University, Lanzhou, 730070

Received: September 30, 2014

Revised: September 30, 2015

Published: February 2016

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Abstract

This paper is concerned with the traveling wave solutions of a reaction-diffusion equation with state-dependent delay. When the birth function is monotone, the existence and nonexistence of monotone traveling wave solutions are established. When the birth function is not monotone, the minimal wave speed of nontrivial traveling wave solutions is obtained. The results are proved by the construction of upper and lower solutions and application of the fixed point theorem.

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Mathematics Subject Classification: Primary: 35K57; Secondary: 35C07; 37C65.

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