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Global existence and nonexistence for diffusive polytropic filtration equations with nonlinear boundary conditions

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Abstract

In this paper, we deal with the global existence and nonexistence of solutions to a diffusive polytropic filtration system with nonlinear boundary conditions. By constructing various kinds of sub- and super-solutions and using the basic properties of M-matrix, we give the necessary and sufficient conditions for global existence of nonnegative solutions, which extend the recent results of Li et al. (Z Angew Math Phys 60:284–298, 2009) and Wang et al. (Nonlinear Anal 71:2134–2140, 2009) to more general equations and simplify their proofs slightly.

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  1. School of Applied Mathematics, University of Electronic Science and Technology of China, 610054, Chengdu, China

    Zhaoyin Xiang

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  1. Zhaoyin Xiang
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Xiang, Z. Global existence and nonexistence for diffusive polytropic filtration equations with nonlinear boundary conditions. Z. Angew. Math. Phys. 61, 467–478 (2010). https://doi.org/10.1007/s00033-009-0028-9

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  • DOI: https://doi.org/10.1007/s00033-009-0028-9

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