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Research Article | Open Access

Simultaneous blow-up of the solution for a singular parabolic system with concentrated sources

Department of MIS, Computer Science, and Mathematics, Texas A&M University-Texarkana, Texarkana, TX 75503, USA
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Abstract

A singular parabolic system with homogeneous Dirichlet boundary conditions and concentrated nonlinear reaction sources was examined. This paper investigated the existence and uniqueness of the solution. The sufficient conditions for the solution being blown up simultaneously in a finite time were determined. In addition, it was shown that the solution blew up everywhere in the domain except boundary points.

Keywords

blow-upDirac delta functionGreen's functionsingular parabolic problem
CLC number: 35K35, 35K55, 35K57, 35K58, 35K61

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AIMS Mathematics
Volume 9 Issue 3,
March 2024
Pages 6951-6963
DOI: 10.3934/math.2024339

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Chan WY. Simultaneous blow-up of the solution for a singular parabolic system with concentrated sources. AIMS Mathematics, 2024, 9(3): 6951-6963. https://doi.org/10.3934/math.2024339

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Received: 28 November 2023
Revised: 15 January 2024
Accepted: 19 January 2024
Published: 15 March 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)