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Travelling wave solutions of a free boundary problem for a two-species competitive model

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  • We study a di usive logistic system with a free boundary in ecology proposed by Mimura, Yamada and Yotsutani [10]. Motivated by the spreading-vanishing dichotomy obtained by Du and Lin [1], we suppose the spreading speed of the free boundary tends to a constant as time tends to in nity and consider the corresponding travelling wave problem. We establish the existence and uniqueness of a travelling wave solution for this free boundary problem.
    Mathematics Subject Classification: 35K57, 35C07, 35R35.


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  • [1]

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    Y. Du and Z. Guo, Spreading-vanishing dichotomy in a diffusive logistic model with a free boundary II, J. Differential Equations, 250 (2011), 4336-4366.doi: 10.1016/j.jde.2011.02.011.


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    Z. Ling, Q. Tang and Z. Lin, A free boundary problem for two-species competitive model in ecology, Nonlinear Anal. Real World Appl., 11 (2010), 1775-1781.doi: 10.1016/j.nonrwa.2009.04.001.


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    A. I. Volpert, V. A. Volpert and V. A. Volpert, "Traveling Wave Solutions of Parabolic Systems," Translations of Mathematical Monographs, 140, Amer. Math. Soc., Providence, 1994.

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