Existence, uniqueness and asymptotic stability of time periodic traveling waves for a periodic Lotka–Volterra competition system with diffusion |
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Authors: | Guangyu Zhao Shigui Ruan |
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Affiliation: | Department of Mathematics, University of Miami, Coral Gables, FL 33124-4250, USA |
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Abstract: | We study the existence, uniqueness, and asymptotic stability of time periodic traveling wave solutions to a periodic diffusive Lotka–Volterra competition system. Under certain conditions, we prove that there exists a maximal wave speed c? such that for each wave speed c?c?, there is a time periodic traveling wave connecting two semi-trivial periodic solutions of the corresponding kinetic system. It is shown that such a traveling wave is unique modulo translation and is monotone with respect to its co-moving frame coordinate. We also show that the traveling wave solutions with wave speed c<c? are asymptotically stable in certain sense. In addition, we establish the nonexistence of time periodic traveling waves for nonzero speed c>c?. |
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Keywords: | MSC: 35B10 35B35 35B40 35C07 35K40 |
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