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

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.