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Asymptotic estimates to non-global solutions of a multi-coupled parabolic system

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Abstract

This paper deals with asymptotic behavior of solutions to a parabolic system, where two heat equations with inner absorptions are multi-coupled via inner sources and boundary flux. We determine four kinds of simultaneous blow-up rates under different dominations of nonlinearities in the model. Two characteristic algebraic systems associated with the problem are introduced to get very simple descriptions for the four simultaneous blow-up rates as well as the known critical exponents, respectively. It is observed that the blow-up rates are independent of the nonlinear inner absorptions.

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Authors and Affiliations

  1. Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024, P. R. China

    Rui Hong Ji & Si Ning Zheng

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  1. Rui Hong Ji
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  2. Si Ning Zheng
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Correspondence to Si Ning Zheng.

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Supported by the National Natural Science Foundation of China (Grant No. 10771024)

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Ji, R.H., Zheng, S.N. Asymptotic estimates to non-global solutions of a multi-coupled parabolic system. Acta. Math. Sin.-English Ser. 24, 1713–1726 (2008). https://doi.org/10.1007/s10114-008-6559-8

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  • DOI: https://doi.org/10.1007/s10114-008-6559-8

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