Spreading speeds and traveling wave solutions in cooperative integral-differential systems

Changbing Hu; Yang Kuang; Bingtuan Li; Hao  Liu

doi:10.3934/dcdsb.2015.20.1663

Article Contents

2015, Volume 20, Issue 6: 1663-1684. Doi: 10.3934/dcdsb.2015.20.1663

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Spreading speeds and traveling wave solutions in cooperative integral-differential systems

1.
Department of Mathematics, University of Louisville, Louisville, KY 40292
2.
School of Mathematics and Statistical Sciences, Arizona State University, Tempe, AZ 85281
3.
School of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287

Received: October 31, 2013

Revised: January 31, 2015

Published: July 2015

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Abstract

We study a cooperative system of integro-differential equations. It is shown that the system in general has multiple spreading speeds, and when the linear determinacy conditions are satisfied all the spreading speeds are the same and equal to the spreading speed of the linearized system. The existence of traveling wave solutions is established via integral systems. It is shown that when the linear determinacy conditions are satisfied, if the unique spreading speed is not zero then it may be characterized as the slowest speed of a class of traveling wave solutions. Some examples are presented to illustrate the theoretical results.

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Mathematics Subject Classification: Primary: 45K05; Secondary: 92D25.

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