General Decay and Blow-Up Results for Nonlinear Fourth-Order Integro-Differential Equation

This study aims at considering an initial-boundary value problem for nonlinear fourth-order viscoelastic equation in a bounded domain. Under suitable conditions of the initial data and of the relaxation function, it is proved that the solution energy is generally decayed. It is also shown that regarding arbitrary positive initial energy, certain solutions blow-up in a finite time.