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

Abstract

The paper is concerned with a second-order abstract semilinear evolution equation with infinite memory and time delay. With the help of the semigroup arguments and under suitable conditions on initial data and the kernel memory function, we state and prove the global existence of solution. Then, we establish the decay rates of the energy using the multiplier method by defining a suitable Lyapunov functional. This work extends previous works with time delay for a much wider class of kernels. We give also some applications to illustrate our results.