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This paper deals with the boundary stabilization problem of a one-dimensionalwave equation with a switching time-delay in the boundary. We show that theproblem is well-posed in the sense of semigroups theory of linear operators.Then, we provide a theoretical and numerical study of the exponential stabilityof the system under an appropriate delay coefficient.

Boundary stabilization of a one-dimensional wave equation by a switching time-delay: a theoretical and numerical study