Feedback stabilization and optimal control for the Cahn-Hilliard equation
Nonlinear Analysis: Theory, Methods & Applications
SIAM Journal on Control and Optimization
Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity
Mathematics of Operations Research
SIAM Journal on Control and Optimization
Computational Methods for Option Pricing (Frontiers in Applied Mathematics) (Frontiers in Applied Mathematics 30)
Adaptive finite element methods for Cahn-Hilliard equations
Journal of Computational and Applied Mathematics
The influence of electric fields on nanostructures-Simulation and control
Mathematics and Computers in Simulation
SIAM Journal on Control and Optimization
A smooth penalty approach and a nonlinear multigrid algorithm for elliptic MPECs
Computational Optimization and Applications
An adaptive finite-element Moreau-Yosida-based solver for a non-smooth Cahn-Hilliard problem
Optimization Methods & Software - Advances in Shape and Topology Optimization: Theory, Numerics and New Applications Areas
Computational Optimization and Applications
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In this paper we study the distributed optimal control for the Cahn-Hilliard system. A general class of free energy potentials is allowed which, in particular, includes the double-obstacle potential. The latter potential yields an optimal control problem of a parabolic variational inequality which is of fourth order in space. We show the existence of optimal controls to approximating problems where the potential is replaced by a mollified version of its Moreau-Yosida approximation. Corresponding first-order optimality conditions for the mollified problems are given. For this purpose a new result on the continuous Fréchet differentiability of superposition operators with values in Sobolev spaces is established. Besides the convergence of optimal controls of the mollified problems to an optimal control of the original problem, we also derive first-order optimality conditions for the original problem by a limit process. The newly derived stationarity system corresponds to a function space version of C-stationarity.