Controllability for a Wave Equation with Moving Boundary

Abstract EN

We investigate the controllability for a one-dimensional wave equation in domains with moving boundary.

This model characterizes small vibrations of a stretched elastic string when one of the two endpoints varies.

When the speed of the moving endpoint is less than 1-1/e, by Hilbert uniqueness method, sidewise energy estimates method, and multiplier method, we get partial Dirichlet boundary controllability.

Moreover, we will give a sharper estimate on controllability time that only depends on the speed of the moving endpoint.