Lower and upper bounds for the blow-up time to a viscoelastic Petrovsky wave equation with variable sources and memory term

Abstract

Under Dirichlet boundary conditions, we consider here a new type of viscoelastic Petrovsky wave equation involving variable sources and memory term We discuss the blow-up in finite time with arbitrary positive initial energy and suitable large initial values if and the relaxation function g satisfies some conditions. Employing a different method for higher bounded positive initial energy, not only finite time blow-up for solutions proved but also the lower and upper bounds for blowing up time are gotten.