Oberseminar Wissenschaftliches Rechnen (Dr. Stefana Anita)

Abstract:

Computational measurement models may involve several uncertain simulation parameters: not only can the material properties of a heterogeneous medium be unknown, but the shape of the structure itself can be uncertain as well. This presentation concerns an optimal control problem (P) related to a nonlinear Fokker-Planck equation. The problem is deeply related to a stochastic optimal control problem (PS) for a McKean-Vlasov equation. The existence of an optimal control is obtained for the deterministic problem (P). The existence of an optimal control is established and necessary optimality conditions are derived for a penalized optimal control problem (Ph) related to a backward Euler approximation of the nonlinear Fokker-Planck equation (with a constant discretization step h). Passing to the limit one derives the necessary optimality conditions for problem (P).

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