General decay for a viscoelastic wave equation of the Kirchhoff type with delay

Abstract

The main goal of this thesis is studing the Asymptotic behavior of solutions to a vis- coelastic Kirchhoff-type plate equation with memory and delay terms, under classical initial

and boundary conditions.first we present necessary mathematical preliminaries. Then,by using energy estimates and suitable assumptions on the damping and relaxation functions, we prove

the global existence. Finally, we establish a general decay result for the total energy by con- structing an appropriate Lyapunov functional. The result shows that the energy decays over

time, illustrating the combined stabilizing effect of damping and memory, even in the presence of delay.