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Research Article | Open Access

Energy solutions to the bi-harmonic parabolic equations

Saleh Almuthaybiri, Tarek Saanouni( )
Department of Mathematics, College of Science, Qassim University, Saudi Arabia
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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.

Keywords

inhomogeneous fourth-order parabolic problemnonlinear equationsglobal/non-global solutions
CLC number: 35K30, 35K25

References

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AIMS Mathematics
Volume 9 Issue 12,
December 2024
Pages 35264-35273
DOI: 10.3934/math.20241675

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Cite this article:
Almuthaybiri S, Saanouni T. Energy solutions to the bi-harmonic parabolic equations. AIMS Mathematics, 2024, 9(12): 35264-35273. https://doi.org/10.3934/math.20241675

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Received: 21 October 2024
Revised: 28 November 2024
Accepted: 02 December 2024
Published: 15 December 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)