Traveling wave solutions for time periodic reaction-diffusion systems

Wei-Jian Bo; Guo Lin; Shigui Ruan

doi:10.3934/dcds.2018189

Article Contents

2018, Volume 38, Issue 9: 4329-4351. Doi: 10.3934/dcds.2018189

This issue Previous Article Topological classification of $Ω$-stable flows on surfaces by means of effectively distinguishable multigraphs Next Article The Hénon equation with a critical exponent under the Neumann boundary condition

Traveling wave solutions for time periodic reaction-diffusion systems

1.
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China
2.
Department of Mathematics, University of Miami, Coral Gables, FL 33146, USA

* Corresponding author: Guo Lin
* Corresponding author: Guo Lin

Received: July 2017

Revised: April 2018

Published: September 2018

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Abstract

This paper deals with traveling wave solutions for time periodic reaction-diffusion systems. The existence of traveling wave solutions is established by combining the fixed point theorem with super- and sub-solutions, which reduces the existence of traveling wave solutions to the existence of super- and sub-solutions. The asymptotic behavior is determined by the stability of periodic solutions of the corresponding initial value problems. To illustrate the abstract results, we investigate a time periodic Lotka-Volterra system with two species by presenting the existence and nonexistence of traveling wave solutions, which connect the trivial steady state to the unique positive periodic solution of the corresponding kinetic system.

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Mathematics Subject Classification: Primary: 45C05, 45M05; Secondary: 92D40.

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