Global Existence, General Decay, and Blow Up of the Solution to the Coupled p -Biharmonic Equation of Hyperbolic Type with Degenerate Damping Terms

Nouri Boumaza (), Billel Gheraibia, Hongwei Zhang and Zayd Hajjej ()
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Nouri Boumaza: Department of Mathematics, Echahid Cheikh Larbi Tebessi University, Tebessa 12000, Algeria
Billel Gheraibia: Laboratory of Mathematics, Informatics and Systems (LAMIS), Echahid Cheikh Larbi Tebessi University, Tebessa 12000, Algeria
Hongwei Zhang: Department of Mathematics, Henan University of Technology, Zhengzhou 450001, China
Zayd Hajjej: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Mathematics, 2025, vol. 13, issue 19, 1-17

Abstract: In this work, we study a nonlinear system of p -Biharmonic hyperbolic equations with degenerate damping and source terms in a bounded domain. Under appropriate assumptions on the initial data and the damping terms, we establish the global existence of solutions. Furthermore, we derive a general decay result, and finally, we prove the occurrence of blow-up for solutions with negative initial energy.

Keywords: p-Biharmonic equation; degenerate damping; global existence; general decay; blow up (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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