Exact boundary controllability for the wave equation with moving boundary domains in a star-shaped hole

Abstract

We consider an exact boundary control problem for the wave equation in a moving bounded domain which has a star-shaped hole. The boundary domain is composed by two disjoint parts, one is the boundary of the hole, which is fixed, and the other one is the external boundary which is moving. The initial data has finite energy and the control obtained is square integrable and is obtained by means of the conormal derivative. We use the method of controllability presented by Russell in [20], and assume that the control acts only in the moving part of the boundary.