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Mathematical Biosciences and Engineering (MBE)
 

Invasion entire solutions in a time periodic Lotka-Volterra competition system with diffusion

Pages: 1187 - 1213, Volume 14, Issue 5/6, October/December 2017      doi:10.3934/mbe.2017061

 
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Li-Jun Du - School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China (email)
Wan-Tong Li - School of Mathematics and Statistics, Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou, Gansu 730000, China (email)
Jia-Bing Wang - School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China (email)

Abstract: This paper is concerned with invasion entire solutions of a monostable time periodic Lotka-Volterra competition-diffusion system. We first give the asymptotic behaviors of time periodic traveling wave solutions at infinity by a dynamical approach coupled with the two-sided Laplace transform. According to these asymptotic behaviors, we then obtain some key estimates which are crucial for the construction of an appropriate pair of sub-super solutions. Finally, using the sub-super solutions method and comparison principle, we establish the existence of invasion entire solutions which behave as two periodic traveling fronts with different speeds propagating from both sides of $x$-axis. In other words, we formulate a new invasion way of the superior species to the inferior one in a time periodic environment.

Keywords:  Time periodic traveling waves, asymptotic behavior, comparison principle, invasion entire solution.
Mathematics Subject Classification:  Primary: 35K57, 35K55; Secondary: 35B15, 92D25.

Received: May 2016;      Accepted: October 2016;      Available Online: May 2017.

 References