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Research Article | Open Access

Blow-up upper and lower bounds for solutions of a class of higher order nonlinear pseudo-parabolic equations

Qianqian Zhu, Yaojun Ye( ), Shuting Chang
Department of Mathematics and Statistics, Zhejiang University of Science and Technology, Hangzhou 310023, China
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Abstract

In this paper, we study the initial boundary value problem for a class of higher-order nonlinear pseudo-parabolic equations with a memory term. First, the blow-up results of the solution when the initial energy is negative or positive are obtained by using concavity analysis, and an upper bound on the blow-up time T ∗ is given. Second, a lower bound on the blow-up time T ∗ is obtained by applying differential inequalities when the solutions blow up.

Keywords

higher order pseudo-parabolic equationmemory termblow-upupper boundlower bound

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Electronic Research Archive
Volume 32 Issue 2,
February 2024
Pages 945-961
DOI: 10.3934/era.2024046

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Cite this article:
Zhu Q, Ye Y, Chang S. Blow-up upper and lower bounds for solutions of a class of higher order nonlinear pseudo-parabolic equations. Electronic Research Archive, 2024, 32(2): 945-961. https://doi.org/10.3934/era.2024046

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Received: 28 August 2023
Revised: 28 November 2023
Accepted: 12 December 2023
Published: 16 January 2024
©2024 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)