Optimal control for a conserved phase field system with a possibly singular potential

DOI10.3934/eect.2018006zbMath1405.49003OpenAlexW2962770483WikidataQ60581954 ScholiaQ60581954MaRDI QIDQ1711849

Gianni Gilardi, Elisabetta Rocca, Pierluigi Colli, Gabriela Marinoschi

Publication date: 18 January 2019

Published in: Evolution Equations and Control Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/eect.2018006

zbMATH Keywords

optimal controloptimality conditionsphase transitionCahn-Hilliard equationphase field systemsingular potentialsadjoint state system

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Nonlinear parabolic equations (35K55) Stefan problems, phase changes, etc. (80A22) Existence theories for optimal control problems involving partial differential equations (49J20) Initial-boundary value problems for higher-order parabolic systems (35K52)

Related Items

Distributed optimal control of the 2D Cahn-Hilliard-Oberbeck-Boussinesq system for nonisothermal viscous two-phase flows, Optimal distributed control of a Allen-Cahn/Cahn-Hilliard system with temperature, Optimal distributed control for a coupled phase-field system, Optimal borel measure-valued controls to the viscous Cahn–Hilliard–Oberbeck–Boussinesq phase-field system on two-dimensional bounded domains, 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, Numerical optimization of the Dirichlet boundary condition in the phase field model with an application to pure substance solidification, Existence of optimal control for Dirichlet boundary optimization in a phase field problem, Optimal control for the coupled chemotaxis-fluid models in two space dimensions, Optimal distributed control for a new mechanochemical model in biological patterns, Optimal control for a chemotaxis-haptotaxis model in two space dimensions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A boundary control problem for the viscous Cahn-Hilliard equation with dynamic boundary conditions
• Non-isothermal viscous Cahn-Hilliard equation with inertial term and dynamic boundary conditions
• A boundary control problem for the pure Cahn-Hilliard equation with dynamic boundary conditions
• A boundary control problem for a possibly singular phase field system with dynamic boundary conditions
• Optimal control for a phase field system with a possibly singular potential
• Compact sets in the space \(L^ p(0,T;B)\)
• Nonlinear system for non-isothermal diffusive phase separation
• Uniqueness and long-time behavior for the conserved phase-field system with memory
• Maximal attractor and inertial sets for a conserved phase field model
• Hysteresis and phase transitions
• Analysis and optimal boundary control of a nonstandard system of phase field equations
• On the conserved phase-field model
• Distributed optimal control of a nonstandard system of phase field equations
• Optimal control problems of phase field system with total variation functional as the interfacial energy
• On the Cahn-Hilliard equation with dynamic boundary conditions and a dominating boundary potential
• Some optimal control problems for a two-phase field model of solidification
• Sharp interface control in a Penrose−Fife model
• Optimal Boundary Control of a Viscous Cahn--Hilliard System with Dynamic Boundary Condition and Double Obstacle Potentials
• The Dynamics of a Conserved Phase Field System: Stefan-like, Hele-Shaw, and Cahn-Hilliard Models as Asymptotic Limits
• Optimal control of a phase field model for solidification
• Robust exponential attractors for Cahn‐Hilliard type equations with singular potentials
• Free Energy of a Nonuniform System. I. Interfacial Free Energy
• Distributed optimal control problems for phase field systems with singular potential
• Optimal control problems of phase relaxation models