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

Huiyang Xu; Huiyang Xu

doi:10.3934/cam.2023008

Communications in Analysis and Mechanics

2023, Volume 15, Issue 2: 132-161. doi: 10.3934/cam.2023008

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Research article

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

Huiyang Xu ^,

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

Received: 23 March 2023 Revised: 24 April 2023 Accepted: 27 April 2023 Published: 05 May 2023
35K58, 35K65

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.
- Finitely degenerate parabolic equation,
- singular potentials,
- local existence,
- potential well,
- global existence,
- blow-up,
- decay estimate
Citation: Huiyang Xu. Existence and blow-up of solutions for finitely degenerate semilinear parabolic equations with singular potentials[J]. Communications in Analysis and Mechanics, 2023, 15(2): 132-161. doi: 10.3934/cam.2023008

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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.

References

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