16.02.2107 13:00 (s.t), We6 6.020
Florian Kruse (Graz)
## Optimal control of semilinear parabolic equations by BV-functions

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This talk addresses parabolic optimal control problems in which the objective promotes controls that are piecewise constant in time. That is, optimal controls for these problems have a particularly simple structure. To achieve this we consider controls that are BV-functions in time and use the total variation norm of their derivatives in the objective. This implies that the objective is nonsmooth. We prove existence of optimal controls, derive first- and second-order optimality conditions, provide error estimates, and develop a semismooth Newton method for their solution. Numerical examples are presented as well.