# Asymptotic limits and optimal control for the Cahn–Hilliard system with convection and dynamic boundary conditions

@article{Gilardi2019AsymptoticLA, title={Asymptotic limits and optimal control for the Cahn–Hilliard system with convection and dynamic boundary conditions}, author={Gianni Gilardi and J{\"u}rgen Sprekels}, journal={Nonlinear Analysis}, year={2019} }

## 13 Citations

### Boundary control problem and optimality conditions for the Cahn–Hilliard equation with dynamic boundary conditions

- MathematicsInt. J. Control
- 2021

This paper is concerned with a boundary control problem for the Cahn–Hilliard equation coupled with dynamic boundary conditions, and restricts the analysis to the case of regular potentials defined on the whole real line, assuming the boundary potential to be dominant.

### Distributed Optimal Control of the 2D Cahn–Hilliard–Oberbeck–Boussinesq System for Nonisothermal Viscous Two-Phase Flows

- Mathematics
- 2021

We analyze a distributed optimal control problem where the state equation is governed by the coupling of the two-dimensional Cahn–Hilliard and Oberbeck–Boussinesq systems modelling incompressible…

### On a transmission problem for equation and dynamic boundary condition of Cahn–Hilliard type with nonsmooth potentials

- MathematicsMathematische Nachrichten
- 2020

This paper is concerned with well‐posedness of the Cahn–Hilliard equation subject to a class of new dynamic boundary conditions. The system was recently derived in Liu–Wu (Arch. Ration. Mech. Anal.…

### Separation property and convergence to equilibrium for the equation and dynamic boundary condition of Cahn–Hilliard type with singular potential

- MathematicsAsymptotic Analysis
- 2021

We consider a class of Cahn–Hilliard equation that models phase separation process of binary mixtures involving nontrivial boundary interactions in a bounded domain with non-permeable wall. The…

### A P ] 3 1 Ju l 2 01 9 Boundary control problem and optimality conditions for the Cahn – Hilliard equation with dynamic boundary conditions

- Mathematics
- 2019

This paper is concerned with a boundary control problem for the Cahn–Hilliard equation coupled with dynamic boundary conditions. In order to handle the control problem, we restrict our analysis to…

### Longtime behavior for a generalized Cahn-Hilliard system with fractional operators.

- Mathematics
- 2019

In this contribution, we deal with the longtime behavior of the solutions to the fractional variant of the Cahn-Hilliard system, with possibly singular potentials, that we have recently investigated…

### Optimal control theory and advanced optimality conditions for a diffuse interface model of tumor growth

- MathematicsESAIM: Control, Optimisation and Calculus of Variations
- 2020

We investigate a distributed optimal control problem for a diffuse interface model for tumor growth. The model consists of a Cahn–Hilliard type equation for the phase field variable, a reaction…

### An asymptotic analysis for a generalized Cahn–Hilliard system with fractional operators

- Mathematics
- 2020

In the recent paper “Well-posedness and regularity for a generalized fractional Cahn–Hilliard system” (Colli et al. in Atti Accad Naz Lincei Rend Lincei Mat Appl 30:437–478, 2019), the same authors…

### Cahn-Hilliard-Brinkman models for tumour growth: Modelling, analysis and optimal control

- Mathematics
- 2020

Phase field models recently gained a lot of interest in the context of tumour growth models. In this work we study several diffuse interface models for tumour growth in a bounded domain with…

### Challenges in Optimal Control of Nonlinear PDE-Systems

- MathematicsOberwolfach Reports
- 2019

The aims of the workshop were to bring together a group of international experts working at the forefront of research in the field, to foster in-depth-discussions crystallizing around a number of keynote presentations as well as discussion groups on focal topics emerging during the workshop, and to establish an (international) exchange forum for problems, techniques and solutions.

## References

SHOWING 1-10 OF 68 REFERENCES

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

- MathematicsSIAM J. Control. Optim.
- 2018

This paper shows existence for the optimal control problem under investigation, proves the Fr\'echet differentiability of the associated control-to-state mapping in suitable Banach spaces and derive the first-order necessary optimality conditions in terms of a variational inequality and the associated adjoint system.

### Optimal Boundary Control of a Viscous Cahn-Hilliard System with Dynamic Boundary Condition and Double Obstacle Potentials

- MathematicsSIAM J. Control. Optim.
- 2015

This paper investigates optimal boundary control problems for Cahn-Hilliard variational inequalities with a dynamic boundary condition involving double obstacle potentials and the Laplace-Beltrami operator and proves existence of optimal controls and derive first-order necessary conditions of optimality.

### Optimal Distributed Control of a Nonlocal Convective Cahn-Hilliard Equation by the Velocity in Three Dimensions

- MathematicsSIAM J. Control. Optim.
- 2015

Recently proved existence, uniqueness, and regularity results are employed for a distributed optimal control problem for a nonlocal convective Cahn--Hilliard equation with degenerate mobility and singular potential in three dimensions of space.

### Optimal boundary control of a nonstandard Cahn-Hilliard system with dynamic boundary condition and double obstacle inclusions

- Mathematics
- 2017

In this paper, we study an optimal boundary control problem for a model for phase separation taking place in a spatial domain that was introduced by P. Podio-Guidugli in Ric. Mat. 55 (2006), pp.…

### On the longtime behavior of a viscous Cahn–Hilliard system with convection and dynamic boundary conditions

- MathematicsJournal of Elliptic and Parabolic Equations
- 2018

AbstractIn this paper, we study the longtime asymptotic behavior of a phase separation process occurring in a three-dimensional domain containing a fluid flow of given velocity. This process is…

### On a Cahn–Hilliard system with convection and dynamic boundary conditions

- Mathematics
- 2017

This paper deals with an initial and boundary value problem for a system coupling equation and boundary condition both of Cahn–Hilliard type; an additional convective term with a forced velocity…

### Optimal velocity control of a convective Cahn-Hilliard system with double obstacles and dynamic boundary conditions: A 'deep quench' approach

- Mathematics
- 2019

In this paper, we investigate a distributed optimal control problem for a convective viscous Cahn-Hilliard system with dynamic boundary conditions. Such systems govern phase separation processes…

### Optimal Control of a Semidiscrete Cahn-Hilliard-Navier-Stokes System

- MathematicsSIAM J. Control. Optim.
- 2014

In this paper, the optimal boundary control of a time-discrete Cahn--Hilliard--Navier--Stokes system is studied. A general class of free energy potentials is considered which, in particular, includes…

### Optimal Control of a Semidiscrete Cahn-Hilliard-Navier-Stokes System with Nonmatched Fluid Densities

- MathematicsSIAM J. Control. Optim.
- 2017

By proposing a suitable time-discretization, energy estimates are proved and the existence of solutions to the primal system and of optimal controls is established for the original problem as well as for a family of regularized problems.

### Distributed Optimal Control of the Cahn-Hilliard System Including the Case of a Double-Obstacle Homogeneous Free Energy Density

- MathematicsSIAM J. Control. Optim.
- 2012

This paper shows the existence of optimal controls to approximating problems where the potential is replaced by a mollified version of its Moreau-Yosida approximation, and derives first-order optimality conditions for the original problem by a limit process.