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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

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

Pages: 1663 - 1684, Volume 20, Issue 6, August 2015      doi:10.3934/dcdsb.2015.20.1663

 
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Changbing Hu - Department of Mathematics, University of Louisville, Louisville, KY 40292, United States (email)
Yang Kuang - School of Mathematics and Statistical Sciences, Arizona State University, Tempe, AZ 85281, United States (email)
Bingtuan Li - Department of Mathematics, University of Louisville, Louisville, KY 40292, United States (email)
Hao Liu - School of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, United States (email)

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.

Keywords:  Integral-differential system, integral system, linear determinacy, spreading speed, traveling wave solution.
Mathematics Subject Classification:  Primary: 45K05; Secondary: 92D25.

Received: November 2013;      Revised: February 2015;      Available Online: June 2015.

 References