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

Billel Gheraibia, Safa M. Mirgani (), Nouri Boumaza, Khaled Zennir and Sultan S. Alodhaibi
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Billel Gheraibia: Department of Mathematics and Computer Science, University of Oum El-Bouaghi, Oum El-Bouaghi 04000, 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
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

Mathematics, 2025, vol. 13, issue 13, 1-16

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.

Keywords: p -Biharmonic-type equation; acoustic boundary conditions; delay term; global existence; decay results; blow-up; nonlinear equations; energy and industry (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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