Boundary controllability and boundary time-varying feedback stabilization of the 1D wave equation in non-cylindrical domains

Abstract

In this paper, we deal with boundary controllability and boundary stabilizability of the 1D wave equation in non-cylindrical domains. By using the characteristics method, we prove under a natural assumption on the boundary functions that the 1D wave equation is controllable and stabilizable from one side of the boundary. Furthermore, the control function and the decay rate of the solution are given explicitly.

Exact Null Controllability of a One-Dimensional Wave Equation with a Mixed Boundary

“…In cylindrical domains, there are many studies on controllability of wave equations. However, not much work was performed on the wave equations defined in non-cylindrical domains ( [1][2][3][4][5][6][7][8][9][10][11][12][13][14]). In [4], exact controllability was studied where the control is put on moving endpoints.…”