Symmetry (Nov 2023)

Blow-Up Analysis for a Reaction–Diffusion System Coupled via <named-content content-type="inline-formula"><inline-formula><math display="inline"><semantics><mrow><msup><mi>L</mi><mi>α</mi></msup></mrow></semantics></math></inline-formula></named-content>-Norm-Type Sources under Positive Boundary Value Conditions

  • Guangsheng Zhong,
  • Qinghua Zhang

DOI
https://doi.org/10.3390/sym15112074
Journal volume & issue
Vol. 15, no. 11
p. 2074

Abstract

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This article mainly deals with the blow-up properties of nonnegative solutions for a reaction–diffusion system coupled with norm-type sources under positive boundary value conditions. The local existence of a nonnegative solution and the comparison principle are given. The criteria for the global existence or finite time blow-up of the solutions are obtained by constructing new functions and utilizing the super- and -sub-solution method. The results reveal a correlation between the blow-up profiles of the solutions and the size of the domain, as well as the positive boundary value.

Keywords