Existence and exponential stability of solutions for transmission system with varying delay in R

Abstract

In the present paper we are going to consider in a one dimension bounded domain a transmission system with a varying delay. Under suitable assumptions on the weights of the damping and the delay terms, we prove the well-possedness and the uniqueness of solution using the semigroup theory. Also we show the exponential stability by introducing an appropriate Lyaponov functional.

Keywords

• wave equation
• transmission problem
• varying delay term
• exponential stability