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Research Article | Open Access

Existence and blow-up of solutions for finitely degenerate semilinear parabolic equations with singular potentials

School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, People's Republic of China
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Abstract

In this article, we investigate the initial-boundary value problem for a class of finitely degenerate semilinear parabolic equations with singular potential term. By applying the Galerkin method and Banach fixed theorem we establish the local existence and uniqueness of the weak solution. On the other hand, by constructing a family of potential wells, we prove the global existence, the decay estimate and the finite time blow-up of solutions with subcritical or critical initial energy.

Keywords

Finitely degenerate parabolic equationsingular potentialslocal existencepotential wellglobal existenceblow-updecay estimate
CLC number: 35K58, 35K65

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Communications in Analysis and Mechanics
Volume 15 Issue 2,
June 2023
Pages 132-161
DOI: 10.3934/cam.2023008

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Cite this article:
Xu H. Existence and blow-up of solutions for finitely degenerate semilinear parabolic equations with singular potentials. Communications in Analysis and Mechanics, 2023, 15(2): 132-161. https://doi.org/10.3934/cam.2023008

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Received: 23 March 2023
Revised: 24 April 2023
Accepted: 27 April 2023
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

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