
Mathematical Biosciences and Engineering, 2017, 14(5&6): 11871213. doi: 10.3934/mbe.2017061.
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Invasion entire solutions in a time periodic LotkaVolterra competition system with diffusion
1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China
Received: , Accepted: , Published:
This paper is concerned with invasion entire solutions of a monostable time periodic LotkaVolterra competitiondiffusion system. We first give the asymptotic behaviors of time periodic traveling wave solutions at infinity by a dynamical approach coupled with the twosided Laplace transform. According to these asymptotic behaviors, we then obtain some key estimates which are crucial for the construction of an appropriate pair of subsuper solutions. Finally, using the subsuper 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 xaxis. 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
Citation: LiJun Du, WanTong Li, JiaBing Wang. Invasion entire solutions in a time periodic LotkaVolterra competition system with diffusion. Mathematical Biosciences and Engineering, 2017, 14(5&6): 11871213. doi: 10.3934/mbe.2017061
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This article has been cited by:
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 2. WeiJian Bo, Guo Lin, Yuanwei Qi, Propagation dynamics of a time periodic diffusion equation with degenerate nonlinearity, Nonlinear Analysis: Real World Applications, 2019, 45, 376, 10.1016/j.nonrwa.2018.07.010
 3. LiJun Du, WanTong Li, ShiLiang Wu, Pulsating fronts and frontlike entire solutions for a reaction–advection–diffusion competition model in a periodic habitat, Journal of Differential Equations, 2019, 10.1016/j.jde.2018.12.029
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Copyright Info: 2017, WanTong Li, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)
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