Remarks on control and inverse problems for PDEs

Abstract

AbstractThis paper deals with recent results and open questions on the control and parameter identification of systems governed by PDEs. Among them, we find a few parabolic and hyperbolic equations, sometimes in the framework of a free-boundary problem. In the considered control problems, we try to govern the behavior of the solution(s) with a good (judicious) choice of the data. On the other hand, in the other (inverse) problems, the goal is to identify the value(s) of unknown data from particular observations of the solutions. We will recall a collection of optimal control, controllability and inverse problem assertions and will explain the arguments of proof. We will also present the results of some numerical experiments. Finally, we will state several open problems that can motivate future research on the subject.