5 research outputs found
A boundary control problem for the viscous Cahn-Hilliard equation with dynamic boundary conditions
A boundary control problem for the viscous Cahn-Hilliard equations with
possibly singular potentials and dynamic boundary conditions is studied and
first order necessary conditions for optimality are proved.
Key words: Cahn-Hilliard equation, dynamic boundary conditions, phase
separation, singular potentials, optimal control, optimality conditions,
adjoint state syste
Optimal distributed control of a nonlocal Cahn-Hilliard/Navier-Stokes system in 2D
We study a diffuse interface model for incompressible isothermal mixtures of
two immiscible fluids coupling the Navier--Stokes system with a convective
nonlocal Cahn--Hilliard equation in two dimensions of space. We apply recently
proved well-posedness and regularity results in order to establish existence of
optimal controls as well as first-order necessary optimality conditions for an
associated optimal control problem in which a distributed control is applied to
the fluid flow.Comment: 32 page
Optimal boundary control of a simplified Ericksen--Leslie system for nematic liquid crystal flows in
In this paper, we investigate an optimal boundary control problem for a two
dimensional simplified Ericksen--Leslie system modelling the incompressible
nematic liquid crystal flows. The hydrodynamic system consists of the
Navier--Stokes equations for the fluid velocity coupled with a convective
Ginzburg--Landau type equation for the averaged molecular orientation. The
fluid velocity is assumed to satisfy a no-slip boundary condition, while the
molecular orientation is subject to a time-dependent Dirichlet boundary
condition that corresponds to the strong anchoring condition for liquid
crystals. We first establish the existence of optimal boundary controls. Then
we show that the control-to-state operator is Fr\'echet differentiable between
appropriate Banach spaces and derive first-order necessary optimality
conditions in terms of a variational inequality involving the adjoint state
variables
A Nonlinear Model Predictive Concept for Control of Two-Phase Flows Governed by the Cahn-Hilliard Navier-Stokes System
Part 5: Flow ControlInternational audienceWe present a nonlinear model predictive framework for closed-loop control of two-phase flows governed by the Cahn-Hilliard Navier-Stokes system. We adapt the concept for instantaneous control from [6,12,16] to construct distributed closed-loop control strategies for two-phase flows. It is well known that distributed instantaneous control is able to stabilize the Burger’s equation [16] and also the Navier-Stokes system [6,12]. In the present work we provide numerical investigations which indicate that distributed instantaneous control also is well suited to stabilize the Cahn-Hilliard Navier-Stokes system