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

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)