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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

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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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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 and Engineering, 2017, 14(5&6): 1187-1213. doi: 10.3934/mbe.2017061

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• 1. Li-Jun Du, Wan-Tong Li, Jia-Bing Wang, Asymptotic behavior of traveling fronts and entire solutions for a periodic bistable competition–diffusion system, Journal of Differential Equations, 2018, 10.1016/j.jde.2018.07.024
• 2. Wei-Jian 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. Li-Jun Du, Wan-Tong Li, Shi-Liang Wu, Pulsating fronts and front-like 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
• 4. Li-Jun Du, Wan-Tong Li, Shi-Liang Wu, Propagation phenomena for a bistable Lotka–Volterra competition system with advection in a periodic habitat, Zeitschrift für angewandte Mathematik und Physik, 2020, 71, 1, 10.1007/s00033-019-1236-6