RAPID EXACT CONTROLLABILITY OF THE WAVE EQUATION BY CONTROLS DISTRIBUTED ON A TIME-VARIANT SUBDOMAIN

Consider the wave equation with distributed controls supported on a subdomain, called control subdomain, which is allowed to be variant in time. For any prescribed time duration, the authors work out a scheme for changing the control subdomain such that the wave equation is exactly controllable on this time duration, where the control subdomain at any time is allowed to have arbitrarily small measure and relatively simple shape.