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Mathematical Biosciences and Engineering

2017, Volume 14, Issue 5&6: 1187-1213. doi: 10.3934/mbe.2017061
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Invasion entire solutions in a time periodic Lotka-Volterra competition system with diffusion

  • 1.
    School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China
  • Received: 01 March 2016 Accepted: 01 October 2016 Published: 01 October 2017

  • MSC : Primary: 35K57, 35K55; Secondary: 35B15, 92D25

  • 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.

    Citation: Li-Jun Du, Wan-Tong Li, Jia-Bing Wang. Invasion entire solutions in a time periodic Lotka-Volterra competition system with diffusion[J]. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1187-1213. doi: 10.3934/mbe.2017061

    Related Papers:

  • 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.


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