Exact Null Controllability of String Equations with Neumann Boundaries

This article focuses on the exact null controllability of a one-dimensional wave equation in noncylindrical domains. Both the fixed endpoint and the moving endpoint are Neumann-type boundary conditions. The control is put on the moving endpoint. When the speed of the moving endpoint is less than the characteristic speed, we can obtain the exact null controllability of this equation by using the Hilbert uniqueness method. In addition, we get a sharper estimate on controllability time that depends on the speed of the moving endpoint.