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Critical Exponents in a Doubly Degenerate Nonlinear Parabolic System with Inner Absorptions

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Abstract

This paper deals with critical exponents for a doubly degenerate nonlinear parabolic system coupled via local sources and with inner absorptions under null Dirichlet boundary conditions in a smooth bounded domain. The author first establishes the comparison principle and local existence theorem for the above problem. Then under appropriate hypotheses, the author proves that the solution either exists globally or blows up in finite time depends on the initial data and the relations of the parameters in the system. The critical exponent of the system is simply described via a characteristic matrix equation introduced.

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Acknowledgments

The author expresses his deepest thanks to the reviewers and the editor for their careful reading and valuable suggestions. This work was partially supported by Chinese Universities Scientific Fund of Ocean University of China (201113008).

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Authors and Affiliations

  1. Department of Mathematics, Ocean University of China, 238 Songling Road, Qingdao, People’s Republic of China

    Jian Wang

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  1. Jian Wang
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Correspondence to Jian Wang.

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Communicated by Norhashidah M. Ali.

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Wang, J. Critical Exponents in a Doubly Degenerate Nonlinear Parabolic System with Inner Absorptions. Bull. Malays. Math. Sci. Soc. 38, 415–435 (2015). https://doi.org/10.1007/s40840-014-0028-6

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  • DOI: https://doi.org/10.1007/s40840-014-0028-6

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