Electronic Journal of Differential Equations,
Vol. 2014 (2014), No. 101, pp. 1-12.

Title: Exact controllability for a wave equation with mixed boundary conditions 
       in a non-cylindrical domain

Authors: Lizhi Cui (Jilin Univ. of Finance and Economics, Changchun, China)
         Hang Gao  (Northeast Normal Univ., Changchun, China)

Abstract:
 In this article we study the exact controllability of  a one-dimensional
 wave equation with mixed boundary conditions in a non-cylindrical domain.
 The fixed endpoint has a Dirichlet-type boundary condition, while the moving
 end has a Neumann-type condition. When the speed of the moving endpoint
 is less than the characteristic speed, the exact controllability of
 this equation is established by Hilbert Uniqueness Method.
 Moreover, we shall give the explicit dependence of the controllability time
 on the speed of the moving endpoint.

Submitted October 15, 2013. Published April 11, 2014.
Math Subject Classifications: 58J45, 35L05.
Key Words: Exact controllability; wave equation; mixed boundary conditions;
           non-cylindrical domain.