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Optimal decay for abstract second-order evolution equation with infinite memory and time-varying delay in Hilbert spaces.
1 : University of Laghouat
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In this paper, we study a second-order abstract evolution equation in Hilbert spaces with infinite memory, time-varying delay and a much larger class of kernel functions. Firstly, we prove well-posedness of solution by using the semigroup arguments and variable norm technique of Kato. Then, we establish an explicit and general decay results of the energy solution by introducing a suitable Lyaponov functional and some properties of the convex functions. This work improves the previous results with finite memory to infinite memory and without time delay/constant delay term to those with time-varying delay.
