Viscoelastic coupled systems of wave equations with past history
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Date
2022-06-10
Journal Title
Journal ISSN
Volume Title
Publisher
UNIVERSITY of M'SILA
Abstract
In this work, two coupled systems for two wave equations have been
considered; In the first system we have made the past history in two equations,
however in the second system we have considered the past history only in the
first equation. Under some hypotheses in given data we have showed the global
existence and uniqueness of solutions of two systems by using the semigroup
theory. After, we have proved the exponential decay for the first system and for
the second system we have obtained the lack exponential decay of solutions,
consequently we have got the optimal polynomial decay.
Description
Keywords
Coupled system of wave equations, Exponential decay, Optimal polynomial decay, Semigroup theory, Past history