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Research Article | Open Access

Finite-time blow-up in semilinear Kirchhoff-type plate equations with distributed delay and polynomial source term

Louiza Dehbi1, Ahlem Merah1, Mohammed Z. Alqarni2, Ibrahim Mekawy3, Mohamed Abdalla4( ), Fares Yazid1
Laboratory of Pure and Applied Mathematics, Amar Telidji University of Laghouat, 03000, Algeria
Department of Mathematics, Faculty of Science, King Khalid University, Abha, Saudi Arabia
Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia
Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt
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Abstract

This article investigates a Kirchhoff problem by introducing a delayed Kirchhoff plate equation with polynomial nonlinearity. For initial data with negative energy, we establish the blow-up of local solutions by employing energy methods together with appropriate functional inequalities.

Keywords

blow-updistributed delayKirchhoff equationpolynomial nonlinearityenergy methodLyapunov functionalnonlinear equation
CLC number: 35B44, 35L05

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AIMS Mathematics
Volume 10 Issue 12,
December 2025
Pages 30773-30784
DOI: 10.3934/math.20251350

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Dehbi L, Merah A, Alqarni MZ, et al. Finite-time blow-up in semilinear Kirchhoff-type plate equations with distributed delay and polynomial source term. AIMS Mathematics, 2025, 10(12): 30773-30784. https://doi.org/10.3934/math.20251350

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Received: 31 October 2025
Revised: 17 December 2025
Accepted: 19 December 2025
Published: 29 December 2025
©2025 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)