Energy solutions to the bi-harmonic parabolic equations

Saleh Almuthaybiri; Tarek Saanouni; Saleh Almuthaybiri; Tarek Saanouni

doi:10.3934/math.20241675

AIMS Mathematics

2024, Volume 9, Issue 12: 35264-35273. doi: 10.3934/math.20241675

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Research article

Energy solutions to the bi-harmonic parabolic equations

Saleh Almuthaybiri ,
Tarek Saanouni ^,

Department of Mathematics, College of Science, Qassim University, Saudi Arabia

Received: 21 October 2024 Revised: 28 November 2024 Accepted: 02 December 2024 Published: 17 December 2024
MSC : 35K30, 35K25

This study explores the threshold of global existence and exponential decay versus finite-time blow-up for solutions to an inhomogeneous nonlinear bi-harmonic heat problem. The novelty is to consider the inhomogeneous source term. The method uses some standard stable sets under the flow of the fourth-order parabolic problem, due to Payne-Sattynger.
- inhomogeneous fourth-order parabolic problem,
- nonlinear equations,
- global/non-global solutions
Citation: Saleh Almuthaybiri, Tarek Saanouni. Energy solutions to the bi-harmonic parabolic equations[J]. AIMS Mathematics, 2024, 9(12): 35264-35273. doi: 10.3934/math.20241675

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Abstract

This study explores the threshold of global existence and exponential decay versus finite-time blow-up for solutions to an inhomogeneous nonlinear bi-harmonic heat problem. The novelty is to consider the inhomogeneous source term. The method uses some standard stable sets under the flow of the fourth-order parabolic problem, due to Payne-Sattynger.

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