Electron. J. Diff. Equ., Vol. 2014 (2014), No. 101, pp. 1-12.

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

Lizhi Cui, Hang Gao

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.

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Lizhi Cui
College of Applied Mathematics
Jilin University of Finance and Economics
Changchun 130117, China
email: cuilz924@126.com
Hang Gao
School of Mathematics and Statistics
Northeast Normal University
Changchun 130024, China
email: hangg@nenu.edu.cn

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