BLOW-UP FOR LOGARITHMIC VISCOELASTIC BOUSSINESQ EQUATIONS WITH DELAYED DISSIPATIVE TERM AND ACOUSTIC BOUNDARY CONDITIONS

Abstract

The current work is devoted to the study of nonlinear viscoelastic wave equations owing a logarithmic source, nonlinear damping and a delay in the velocity with acoustic boundary conditions for which we provide a blow-up criterion. By the use of an energy method, we prove that the solution with negative initial energy blows up after finite time.Moreover, we examine the blow-up time upper and lower bounds.