Prof. Dr. Boris Vexler
In this talk we consider optimal control problem governed by elliptic equation and parabolic equations, where the control variable lies in a measure space. Such formulations lead to a sparse structure of the optimal control, which provides among other things an elegant way to attack problems of optimal source placement as well as point source identification problems. We discuss in details the functional analytic settings of such problems and the regularity issues of the optimal solutions. Moreover, we present a discretization concept and prove a priori error estimates for the discretization error, which significantly improve the estimates from the literature. Numerical examples for elliptic and parabolic problems in two and three space dimensions illustrate our results.
Datum: 03.07.2014, Raum: G03-106, Zeit: 17:00