Deutsch Intern
Dynamics and Control

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{\displaystyle \infty }, and consequently standard optimality conditions are available.

joint work with Eduardo Casas (Santander)