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Global Existence and Finite Time Blow-up for a Reaction-Diffusion System with Three Components

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Abstract

This paper concerns global existence and finite time blow-up behavior of positive solutions for a nonlinear reaction-diffusion system with different diffusion coefficients. By use of algebraic matrix theory and modern analytical theory, we extend results of Wang (Z. Angew. Math. Phys. 51:160–167, 2000) to a more general system. Furthermore, we give a complete answer to the open problem which was brought forward in Wang (Z. Angew. Math. Phys. 51:160–167, 2000).

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Acknowledgements

The authors are grateful to the reviewer for his careful reading and useful comments. Particularly, it is reviewer’s suggestion that make us first pay attention to different diffusion coefficients. The authors are also appreciated for fund support from the NSFC Grant no. 11171064, the NSFC Grant no. 11626072, the NSF of Jiangsu Province Grant no. BK2011583 and the QingLan Engineering Foundation colleges and universities in Jiangsu province.

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Authors and Affiliations

  1. School of Mathematics, Southeast University, Nanjing, 210096, P.R. China

    Huiling Li

  2. Department of Mathematics, Harbin Engineering University, Harbin, 150001, P.R. China

    Yang Zhang

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  1. Huiling Li
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  2. Yang Zhang
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Correspondence to Huiling Li or Yang Zhang.

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Li, H., Zhang, Y. Global Existence and Finite Time Blow-up for a Reaction-Diffusion System with Three Components. Acta Appl Math 151, 121–148 (2017). https://doi.org/10.1007/s10440-017-0105-6

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  • DOI: https://doi.org/10.1007/s10440-017-0105-6

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