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

Authors : Houria Chellaoua

Pages : 7-25

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Publication Date : 2020-06-30

Article Type : Other

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