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Research Article | Open Access

Upper bounds of blowup time for nonlinear extensible beam equations

Tiantian Pang1, Zhenshan Wang1( ), Weipeng Wu2
College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China
College of Software, Harbin Institute of Information Technology, Harbin 150431, China
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Abstract

This paper aims to investigate the initial boundary value problem for a class of Kirchhoff-type wave equations modified by Woinowsky-Krieger models, which can be used to describe the nonlinear extensible beam. Using the concave property of the function and a differential inequality, we estimate the upper bounds of the blowup time of the blowup solution at subcritical, critical, and high initial energy levels.

Keywords

extensible beam equationKirchhoff-type wave equationupper bounds of the blowup time

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Electronic Research Archive
Volume 33 Issue 9,
September 2025
Pages 5701-5718
DOI: 10.3934/era.2025253

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Pang T, Wang Z, Wu W. Upper bounds of blowup time for nonlinear extensible beam equations. Electronic Research Archive, 2025, 33(9): 5701-5718. https://doi.org/10.3934/era.2025253

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Received: 31 December 2024
Revised: 29 August 2025
Accepted: 02 September 2025
Published: 25 September 2025
©2025 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)