Optimal placement of sensors and actuators for waves,   Enrique Zuazua,   BCAM and Ikerbasque, Spain,  Tue, 17 December, 2013,   11:00 a.m. A-207


The efficiency of control mechanisms often depends on the placement of actuators and censoring devices. This lecture is devoted to discuss this important technological issue in the context of wave propagation. Using Fourier series representations the problem can be recast as an optimal design one involving all the spectrum of the Laplacian. We shall develop a complete theory allowing to distinguish, depending on the complexity of the data to be observed and controlled, cases in which the solution is a classical set constituted by a finite number of sub-intervals, from others in which the optimal set is of Cantor type or those when relaxation occurs. These results will be illustrated by numerical simulations. The lecture is based on recent joint work in collaboration with Y. Privat an E. Trélat. Avoiding unnecessary technicalities it will be addressed to a large audience