Oberseminar "Dynamische Systeme und Kontrolltheorie" - Prof. Dr. Daniel Wachsmuth
Existence of Solutions to Control Problems of Semilinear Partial Differential Equations
Date: | 04/26/2024, 2:30 PM - 3:30 PM |
Category: | Veranstaltung |
Location: | Hubland Nord, Geb. 40, 01.003 |
Speaker: | Prof. Dr. Daniel Wachsmuth, Institut für Mathematik, Universität Würzburg |
We study optimal control problems of semilinear elliptic and parabolic equations. A tracking cost functional, quadratic in the control and state variables, is considered. No control constraints are imposed. We prove that the corresponding state equations are well-posed for controls in L2. However, it is well-known that in the L2 framework the mappings involved in the control problem are not Frechet differentiable in general, which makes any analysis of the optimality conditions challenging. Nevertheless, we prove that every L2 optimal control belongs to L, and consequently standard optimality conditions are available.
joint work with Eduardo Casas (Santander)