Deutsch Intern
Dynamics and Control

"cancelled" - Oberseminar "Dynamische Systeme und Kontrolltheorie" - Prof. Dr. Daniel Wachsmuth

Existence of Solutions to Control Problems of Semilinear Partial Differential Equations - joint work with Eduardo Casas (Santander)
Date: 01/26/2024, 2:00 PM - 3:00 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 $L^2$. However, it is well-known that in the $L^2$ 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 $L^2$ optimal control belongs to $L^\infty$, and consequently standard optimality conditions are available.