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

Year 2020, Volume: 2 Issue: 1, 7 - 25, 30.06.2020

Houria Chellaoua

Abstract

In this paper, we consider a second-order abstract semilinear evolution equation with past
history 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 is
also established defining a suitable Lyapunov functional. This work extends previous works
with time delay for a much wider class of kernels. Some applications are also given to illustrate
the result.

Keywords

Abstract evolution equation, Past history, Time delay

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