Electronic Journal of Differential Equations, Vol. 2021 (2021), No. 49, pp. 1-12.

Title: Exact boundary controllability for the wave equation with moving boundary domains 
       in a star-shaped hole
       
Author: Ruikson S. O. Nunes (Federal Univ. of Mato Grosso, Cuiaba, Brazil)

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.


Submitted August 16, 2020. Published June 01, 2021.
Math Subject Classifications: 35L05, 35L20, 35L53, 35B40, 93B05, 49J20.
Key Words: Wave equation; energy decay; exact boundary controllability;
           non-cylindrical domains; holed domains.