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Asymptotic estimate of solutions in a 4th-order parabolic equation with the Frobenius norm of a Hessian matrix

Part of: Parabolic equations and systems Partial differential equations

Published online by Cambridge University Press:  25 November 2024

Ke Li ,
Bingchen Liu Open the ORCID record for Bingchen Liu [Opens in a new window]  and
Jiaxin Dou
Ke Li
Affiliation:
College of Science, China University of Petroleum, Qingdao 266580, P.R. China
Bingchen Liu*
Affiliation:
College of Science, China University of Petroleum, Qingdao 266580, P.R. China
Jiaxin Dou
Affiliation:
College of Science, China University of Petroleum, Qingdao 266580, P.R. China
*
e-mail: bcliu@upc.edu.cn
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Abstract

This paper deals with a 4th-order parabolic equation involving the Frobenius norm of a Hessian matrix, subject to the Neumann boundary conditions. Some threshold results for blow-up or global or extinction solutions are obtained through classifying the initial energy and the Nehari energy. The bounds of blow-up time, decay estimates, and extinction rates are studied, respectively.

Keywords

4th-order parabolic equationHessian matrixglobal existenceblow-up timeextinction rate

MSC classification

Primary: 35K25: Higher-order parabolic equations 35A01: Existence problems 35B40: Asymptotic behavior of solutions 35B44: Blow-up
Type
Article
Information
Canadian Mathematical Bulletin , Volume 68 , Issue 1 , March 2025 , pp. 91 - 108
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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