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Critical curves and non-extinction conditions for a 2-dimensional non-Newtonian polytropic filtration equations coupled via nonlinear boundary flux

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Abstract

This paper deals with the exterior problem for a 2-dimensional non-Newtonian polytropic filtration equations coupled via nonlinear boundary flux. The critical global existence curve is determined and the critical curve of Fujita type is conjectured with the aid of some new results. In particular, an interesting phenomenon is shown: the critical Fujita curve is quite different from the known results for dimension \(N=1\), it depends not only on the parameters in the problem, but also on the dimension \(N=2\). In addition, the detailed non-extinction conditions of solutions are also given.

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Acknowledgments

The authors would like to express their many thanks to the Editor and Reviewers for their constructive suggestions to improve the previous version of this paper. Project supported by National Natural Science Foundation of China (No. 11461076), Universities and colleges research foundation of Guangxi (No. ZD2014106).

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  1. Institute of Mathematics and Information Science, Yulin Normal University, Yulin, 537000, China

    Zhengqiu Ling

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  1. Zhengqiu Ling
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Ling, Z. Critical curves and non-extinction conditions for a 2-dimensional non-Newtonian polytropic filtration equations coupled via nonlinear boundary flux. J. Appl. Math. Comput. 51, 53–66 (2016). https://doi.org/10.1007/s12190-015-0890-x

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  • DOI: https://doi.org/10.1007/s12190-015-0890-x

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