Existence, Decay, and Blow-up of Solutions for a Weighted m-Biharmonic Equation with Nonlinear Damping and Source Terms

Abstract

In this paper, we consider the weighted m-biharmonic equation with nonlinear damping and source terms. We proved the global existence of solutions. Later, the decay of the energy is established by using Nakao’s inequality. Finally, we proved the blow-up of solutions in finite time.