Professor Hyungchun Lee of Dept. of Mathematics, Ajou University, South Korea |

Title: Uncertainty quantification for partial differential equations and their optimal control problems |

Abstract: In this talk, we consider UQ (Uncertainty quantification) and optimal control problems for partial differential equation with random inputs. First we introduce a general approach of studying UQ and then consider some optimal control problems.
To determine an applicable deterministic control $\hat{f}(x)$, we consider the four cases which we compare for efficiency and feasibility. We prove the existence of optimal states, adjoint states and optimality conditions for each cases. We also derive the optimality systems for the four cases. The optimality system is then discretized by a standard finite element method and sparse grid collocation method for physical space and probability space, respectively. The numerical experiments are performed for their efficiency and feasibility. |

# Monday, Feb 11, 11:00AM-12:00 Noon, Conference room

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