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

Wenyuan Ma and Baoqiang Yan ()
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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

Mathematics, 2023, vol. 11, issue 9, 1-22

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.

Keywords: nonlocal sources; nonlinear boundary conditions; global existence; blow-up profile (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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