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

Louiza Dehbi; Ahlem Merah; Mohammed Z. Alqarni; Ibrahim Mekawy; Mohamed Abdalla; Fares Yazid; Louiza Dehbi; Ahlem Merah; Mohammed Z. Alqarni; Ibrahim Mekawy; Mohamed Abdalla; Fares Yazid

doi:10.3934/math.20251350

AIMS Mathematics

2025, Volume 10, Issue 12: 30773-30784. doi: 10.3934/math.20251350

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Research article

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

1.
Laboratory of Pure and Applied Mathematics, Amar Telidji University of Laghouat, 03000, Algeria
2.
Department of Mathematics, Faculty of Science, King Khalid University, Abha, Saudi Arabia
3.
Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia
4.
Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt

Received: 31 October 2025 Revised: 17 December 2025 Accepted: 19 December 2025 Published: 29 December 2025
MSC : 35B44, 35L05

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.
- blow-up,
- distributed delay,
- Kirchhoff equation,
- polynomial nonlinearity,
- energy method,
- Lyapunov functional,
- nonlinear equation
Citation: Louiza Dehbi, Ahlem Merah, Mohammed Z. Alqarni, Ibrahim Mekawy, Mohamed Abdalla, Fares Yazid. Finite-time blow-up in semilinear Kirchhoff-type plate equations with distributed delay and polynomial source term[J]. AIMS Mathematics, 2025, 10(12): 30773-30784. doi: 10.3934/math.20251350

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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.

References

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