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Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries

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Abstract

This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries. By using super-and sub-solution techniques, we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively, and then give the necessary and sufficient conditions that two components u and ν blow up simultaneously. Finally, the uniform blow-up profiles in the interior are presented.

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Authors and Affiliations

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

    Ling-hua Kong

  2. Department of Mathematics, Southeast University, Nanjing, 210018, China

    Ming-xin Wang

  3. Department of Mathematics, Xuzhou Normal University, Xuzhou, 221116, China

    Ming-xin Wang

Authors
  1. Ling-hua Kong
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  2. Ming-xin Wang
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Corresponding author

Correspondence to Ling-hua Kong.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 10471013, 10471022), and the Ministry of Education of China Science and Technology Major Projects (Grant No. 104090)

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Kong, Lh., Wang, Mx. Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries. SCI CHINA SER A 50, 1251–1266 (2007). https://doi.org/10.1007/s11425-007-0105-5

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  • DOI: https://doi.org/10.1007/s11425-007-0105-5

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