Well‐posedness and energy decay of solutions to a wave equation with a general boundary control of diffusive type

Abbes Benaissa and Said Rafa

Mathematische Nachrichten, 2019, vol. 292, issue 8, 1644-1673

Abstract: In this paper, we study well‐posedness and asymptotic stability of a wave equation with a general boundary control condition of diffusive type. We prove that the system lacks exponential stability. Furthermore, we show an explicit and general decay rate result, using the semigroup theory of linear operators and an estimate on the resolvent of the generator associated with the semigroup.

Date: 2019
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