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Global Existence and Uniform Blow-Up to a Nonlocal Parabolic System with Nonlinear Boundary Conditions Arising in a Thermal Explosion Theory

Author

Listed:
  • Wenyuan Ma

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China)

  • Baoqiang Yan

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China)

Abstract

This paper deals with a nonlinear nonlocal parabolic system with nonlinear heat-loss boundary conditions, which arise in the thermal explosion model. Firstly, we prove a comparison principle for some kinds of parabolic systems under nonlinear boundary conditions. Using this, we improve a new theorem of the sub-and-super solution. Secondly, based on the new sub-and-super solution theorem, the sufficient conditions that the solution exists and blows up uniformly in finite time are presented. Then, we generalize some of the lemmas related to uniform blow-up solutions, which are used to introduce the uniform blow-up profiles of solutions. Finally, we give several numerical simulations to illustrate the existence and uniform blow-up of solutions.

Suggested Citation

  • Wenyuan Ma & Baoqiang Yan, 2023. "Global Existence and Uniform Blow-Up to a Nonlocal Parabolic System with Nonlinear Boundary Conditions Arising in a Thermal Explosion Theory," Mathematics, MDPI, vol. 11(9), pages 1-22, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:1993-:d:1130812
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    References listed on IDEAS

    as
    1. Yansheng Liu, 2013. "Positive Solutions Using Bifurcation Techniques for Boundary Value Problems of Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, November.
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