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Global Existence, General Decay, and Blow up of Solution for a p -Biharmonic Equation of Hyperbolic Type with Delay and Acoustic Boundary Conditions

Author

Listed:
  • Billel Gheraibia

    (Department of Mathematics and Computer Science, University of Oum El-Bouaghi, Oum El-Bouaghi 04000, Algeria
    Laboratory of Mathematics, Informatics and Systems (LAMIS), Echahid Cheikh Larbi Tebessi University, Tebessa 12000, Algeria)

  • Safa M. Mirgani

    (Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia)

  • Nouri Boumaza

    (Laboratory of Mathematics, Informatics and Systems (LAMIS), Echahid Cheikh Larbi Tebessi University, Tebessa 12000, Algeria
    Department of Mathematics, Echahid Cheikh Larbi Tebessi University, Tebessa 12000, Algeria)

  • Khaled Zennir

    (Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia)

  • Sultan S. Alodhaibi

    (Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia)

Abstract

The objective of this work is to investigate the global existence, general decay and blow-up results for a class of p -Biharmonic-type hyperbolic equations with delay and acoustic boundary conditions. The global existence of solutions has been obtained by potential well theory and the general decay result of energy has been established, in which the exponential decay and polynomial decay are only special cases, by using the multiplier techniques combined with a nonlinear integral inequality given by Komornik. Finally, the blow-up of solutions is established with positive initial energy. To our knowledge, the global existence, general decay, and blow-up result of solutions to p -Biharmonic-type hyperbolic equations with delay and acoustic boundary conditions has not been studied.

Suggested Citation

  • Billel Gheraibia & Safa M. Mirgani & Nouri Boumaza & Khaled Zennir & Sultan S. Alodhaibi, 2025. "Global Existence, General Decay, and Blow up of Solution for a p -Biharmonic Equation of Hyperbolic Type with Delay and Acoustic Boundary Conditions," Mathematics, MDPI, vol. 13(13), pages 1-16, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2104-:d:1688445
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    References listed on IDEAS

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    1. Li, Chan & Liang, Jin & Xiao, Ti-Jun, 2018. "Polynomial stability for wave equations with acoustic boundary conditions and boundary memory damping," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 593-601.
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    Cited by:

    1. Nouri Boumaza & Billel Gheraibia & Hongwei Zhang & Zayd Hajjej, 2025. "Global Existence, General Decay, and Blow Up of the Solution to the Coupled p -Biharmonic Equation of Hyperbolic Type with Degenerate Damping Terms," Mathematics, MDPI, vol. 13(19), pages 1-17, October.
    2. Billel Gheraibia & Safa M. Mirgani & Nouri Boumaza & Khaled Zennir, 2025. "On the Existence and Behavior of Solution for p(x)‐Biharmonic‐Type Hyperbolic Equation With Nonlinear Damping and Variable Exponent Source," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).

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