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Pattern Formations for a Strong Interacting Free Boundary Problem

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Abstract

In this paper we consider the system of reaction-diffusion-advection equations with a free boundary, which arises in a competition ecological model in heterogeneous environment. In strong competition case, we study the influence of competition rates on the long time behavior of solutions and prove that two species spatially segregate as the competition rates become large. Besides, by using a blow up method, we obtain the uniform Hölder bounds for solutions of the system.

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Acknowledgements

The authors would like to express their sincere thanks to the anonymous reviewers for their helpful comments and suggestions. The work is partially supported by PRC grant NSFC 11371310, 11401515 and 11601224.

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Authors and Affiliations

  1. School of Mathematical Science, Yangzhou University, Yangzhou, 225002, China

    Ling Zhou & Zuhan Liu

  2. Dept. of Mathematical, Nanjing Univ. of Finance & Economics, Nanjing, 210023, China

    Shan Zhang

Authors
  1. Ling Zhou
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  2. Shan Zhang
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  3. Zuhan Liu
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Correspondence to Ling Zhou.

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Zhou, L., Zhang, S. & Liu, Z. Pattern Formations for a Strong Interacting Free Boundary Problem. Acta Appl Math 148, 121–142 (2017). https://doi.org/10.1007/s10440-016-0081-2

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  • DOI: https://doi.org/10.1007/s10440-016-0081-2

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