Optimal Velocity Control of a Viscous Cahn--Hilliard System with Convection and Dynamic Boundary Conditions

DOI10.1137/17M1146786zbMath1391.49039arXiv1709.02335OpenAlexW2963472324MaRDI QIDQ4641755

Gianni Gilardi, Pierluigi Colli, Juergen Sprekels

Publication date: 18 May 2018

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.02335

zbMATH Keywords

optimality conditionsCahn-Hilliard systemdynamic boundary conditionsadjoint state systemconvection termoptimal velocity control

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Stefan problems, phase changes, etc. (80A22) Forced convection (76R05) Dynamic and nonequilibrium phase transitions (general) in statistical mechanics (82C26) Higher-order parabolic equations (35K25) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61)

Related Items

Asymptotic limits and optimal control for the Cahn-Hilliard system with convection and dynamic boundary conditions ⋮ Optimal velocity control of a convective Cahn-Hilliard system with double obstacles and dynamic boundary conditions: a `deep quench' approach ⋮ The Cahn--Hilliard Equation with Forward-Backward Dynamic Boundary Condition via Vanishing Viscosity ⋮ Optimal control problems with sparsity for tumor growth models involving variational inequalities ⋮ Optimal distributed control of two-dimensional nonlocal Cahn-Hilliard-Navier-Stokes systems with degenerate mobility and singular potential ⋮ Optimal treatment for a phase field system of Cahn-Hilliard type modeling tumor growth by asymptotic scheme ⋮ Optimal distributed control of an extended model of tumor growth with logarithmic potential ⋮ Optimal distributed control of a generalized fractional Cahn-Hilliard system ⋮ Optimal control problem for the Cahn-Hilliard/Allen-Cahn equation with state constraint ⋮ Well-posedness and optimal control for a viscous Cahn-Hilliard-Oono system with dynamic boundary conditions ⋮ Second-order sufficient conditions for sparse optimal control of singular Allen-Cahn systems with dynamic boundary conditions ⋮ Second-Order Sufficient Conditions in the Sparse Optimal Control of a Phase Field Tumor Growth Model with Logarithmic Potential ⋮ Optimal control theory and advanced optimality conditions for a diffuse interface model of tumor growth ⋮ Nonlocal Phase Field Models of Viscous Cahn–Hilliard Type ⋮ Deep quench approximation and optimal control of general Cahn-Hilliard systems with fractional operators and double obstacle potentials ⋮ On the longtime behavior of a viscous Cahn-Hilliard system with convection and dynamic boundary conditions ⋮ Optimal medication for tumors modeled by a Cahn-Hilliard-Brinkman equation ⋮ Optimal distributed control of a Cahn-Hilliard-Darcy system with mass sources ⋮ Analysis and optimal velocity control of a stochastic convective Cahn-Hilliard equation ⋮ Well-posedness and optimal control for a Cahn-Hilliard-Oono system with control in the mass term ⋮ Boundary control problem and optimality conditions for the Cahn–Hilliard equation with dynamic boundary conditions

Cites Work

• Unnamed Item
• Unnamed Item
• A boundary control problem for the viscous Cahn-Hilliard equation with dynamic boundary conditions
• Equation and dynamic boundary condition of Cahn-Hilliard type with singular potentials
• Distributed optimal control of a nonstandard nonlocal phase field system with double obstacle potential
• Optimal control for the convective Cahn-Hilliard equation in 2D case
• A boundary control problem for the pure Cahn-Hilliard equation with dynamic boundary conditions
• Compact sets in the space \(L^ p(0,T;B)\)
• Well-posedness of the weak formulation for the phase-field model with memory
• A boundary control problem for the equation and dynamic boundary condition of Cahn-Hilliard type
• A goal-oriented dual-weighted adaptive finite element approach for the optimal control of a nonsmooth Cahn-Hilliard-Navier-Stokes system
• Cahn-Hilliard equation with dynamic boundary conditions and mass constraint on the boundary
• Optimal boundary control of a nonstandard viscous Cahn-Hilliard system with dynamic boundary condition
• Optimal control problem for Cahn-Hilliard equations with state constraint
• Optimal Distributed Control of a Nonlocal Cahn--Hilliard/Navier--Stokes System in Two Dimensions
• Optimal control of the convective Cahn–Hilliard equation
• Distributed Optimal Control of the Cahn–Hilliard System Including the Case of a Double-Obstacle Homogeneous Free Energy Density
• Optimal Boundary Control of a Viscous Cahn--Hilliard System with Dynamic Boundary Condition and Double Obstacle Potentials
• Recent Results on the Cahn - Hilliard Equation with Dynamic Boundary Conditions
• On A Class Of Doubly Nonlinear Evolution Equations
• 3. Distributed and boundary control problems for the semidiscrete Cahn–Hilliard/Navier–Stokes system with nonsmooth Ginzburg–Landau energies
• Optimal Control of a Semidiscrete Cahn--Hilliard--Navier--Stokes System with Nonmatched Fluid Densities
• Optimal distributed control of a diffuse interface model of tumor growth
• Optimal Control of a Semidiscrete Cahn--Hilliard--Navier--Stokes System
• Optimal Distributed Control of a Nonlocal Convective Cahn--Hilliard Equation by the Velocity in Three Dimensions
• Second-order analysis of a boundary control problem for the viscous Cahn--Hilliard equation with dynamic boundary condition
• Analytic semigroups and optimal regularity in parabolic problems