Structural calculations and propagation modeling of growing networks based on continuous degree
Global dynamics of a vector-host epidemic model with age of infection
October 2017, 14(5&6): 1187-1213. doi: 10.3934/mbe.2017061
Invasion entire solutions in a time periodic Lotka-Volterra competition system with diffusion
Li-Jun Du 1, , Wan-Tong Li 1,, and Jia-Bing Wang 1,
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China
Received March 2016 Accepted October 2016 Published May 2017
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.
Citation: Li-Jun Du, Wan-Tong Li, Jia-Bing Wang. Invasion entire solutions in a time periodic Lotka-Volterra competition system with diffusion. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1187-1213. doi: 10.3934/mbe.2017061
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Li-Jun Du Wan-Tong Li Jia-Bing Wang