Abstract
This paper is addressed to a study of the controllability for a one-dimensional wave equation in domains with moving boundary. This equation characterizes the motion of a string with a fixed endpoint and the other moving one. When the speed of the moving endpoint is less than the characteristic speed, by the Hilbert Uniqueness Method, the exact controllability of this equation is established. Also, an explicit dependence of the controllability time on the speed of the moving endpoint is given. Moreover, when the speed of the moving endpoint is equal to the characteristic speed, by a constructive method, we characterize a target set for the exact controllability with smooth controllers.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
