Optimal Control of Quasilinear Parabolic PDEs with State-Constraints
Fabian Hoppe, Ira Neitzel · SIAM Journal on Control and Optimization · 2022
We discuss state-constrained optimal control of a quasilinear parabolic partial differential equation. Existence of optimal controls and first-order necessary optimality conditions are derived for a rather general setting including pointwise in time and space constraints on the state. Second-order sufficient optimality conditions are obtained for averaged-in-time and pointwise in space state-constraints under general regularity assumptions for the equation. Moreover, we provide second-order sufficient optimality conditions also in the case of pointwise in space and time state-constraints, but in return for a more regular setting for the equation.