Electron. J. Diff. Equ., Vol. 2014 (2014), No. 212, pp. 1-11.

Existence and exponential decay of solutions for transmission problems with delay

Aissa Benseghir

Abstract:
In this article we consider a transmission problem in a bounded domain with a delay term in the first equation. Under suitable assumptions on the weight of the damping and the weight of the delay, we prove the existence and the uniqueness of the solution using the semigroup theory. Also we show the exponential stability of the solution by introducing a suitable Lyaponov functional.

Submitted July 14, 2014. Published October 14, 2014.
Math Subject Classifications: 35B37, 35L55, 74D05, 93D15, 93D20.
Key Words: Wave equation; transmission problem; delay term; exponential stability.

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Aissa Benseghir
Université Ferhat Abbas de Sétif, Algeria
email: aissa5919@yahoo.fr

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