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Global existence and blowup of solutions to a free boundary problem for mutualistic model

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Abstract

This article is concerned with a system of semilinear parabolic equations with a free boundary, which arises in a mutualistic ecological model. The local existence and uniqueness of a classical solution are obtained. The asymptotic behavior of the free boundary problem is studied. Our results show that the free problem admits a global slow solution if the inter-specific competitions are strong, while if the inter-specific competitions are weak there exist the blowup solution and global fast solution.

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Authors and Affiliations

  1. Department of Mathematics, Pohang University of Science and Technology, Pohang, 790-784, Korea

    KwangIk Kim

  2. School of Mathematical Sciences, Yangzhou University, Yangzhou, 225002, China

    ZhiGui Lin & Zhi Ling

Authors
  1. KwangIk Kim
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  2. ZhiGui Lin
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  3. Zhi Ling
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Correspondence to ZhiGui Lin.

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Kim, K., Lin, Z. & Ling, Z. Global existence and blowup of solutions to a free boundary problem for mutualistic model. Sci. China Math. 53, 2085–2095 (2010). https://doi.org/10.1007/s11425-010-4007-6

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  • DOI: https://doi.org/10.1007/s11425-010-4007-6

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