Stability result for an abstract time delayed evolution equation with arbitrary decay of viscoelasticity

Abstract

In this paper, we consider a second-order abstract semilinear evolution equation with pasthistory and time delay. Under suitable conditions on initial data and the kernel memory function, we prove the well-posedness by using the semigroup arguments. The stability result isalso established defining a suitable Lyapunov functional. This work extends previous workswith time delay for a much wider class of kernels. Some applications are also given to illustratethe result.