A boundary control problem for the viscous Cahn-Hilliard equation with dynamic boundary conditions
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Publication:282069
DOI10.1007/s00245-015-9299-zzbMath1338.35227arXiv1407.3916OpenAlexW2148663080MaRDI QIDQ282069
Pierluigi Colli, Gianni Gilardi, Juergen Sprekels
Publication date: 12 May 2016
Published in: Applied Mathematics and Optimization (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1407.3916
optimal controloptimality conditionsCahn-Hilliard equationphase separationsingular potentialsdynamic boundary conditionsadjoint state system
Nonlinear parabolic equations (35K55) Dynamic and nonequilibrium phase transitions (general) in statistical mechanics (82C26)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Maximal regularity and asymptotic behavior of solutions for the Cahn-Hilliard equation with dynamic boundary conditions
- Optimal control for the convective Cahn-Hilliard equation in 2D case
- Models of phase segregation and diffusion of atomic species on a lattice
- On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions
- On the Cahn-Hilliard equation
- Compact sets in the space \(L^ p(0,T;B)\)
- The Cahn-Hilliard equation with dynamic boundary conditions.
- Convergence to equilibrium for the Cahn-Hilliard equation with dynamic boundary conditions
- Viscous Cahn-Hilliard equation. II: Analysis
- Analysis and optimal boundary control of a nonstandard system of phase field equations
- Global solution to the Allen-Cahn equation with singular potentials and dynamic boundary conditions
- Distributed optimal control of a nonstandard system of phase field equations
- On the Cahn-Hilliard equation with dynamic boundary conditions and a dominating boundary potential
- A deep quench approach to the optimal control of an Allen-Cahn equation with dynamic boundary conditions and double obstacles
- The existence of a global solution for one dimensional compressible viscous micropolar fluid with non-homogeneous boundary conditions for temperature
- Sulle equazioni differenziali astratte lineari del primo e del secondo ordine negli spazi di Hilbert
- The Allen-Cahn equation with dynamic boundary conditions and mass constraints
- Optimal Control of an Allen--Cahn Equation with Singular Potentials and Dynamic Boundary Condition
- 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
- Convergence to steady states of solutions of the Cahn–Hilliard and Caginalp equations with dynamic boundary conditions
- Robust exponential attractors for Cahn‐Hilliard type equations with singular potentials
- A Nonlinear Model Predictive Concept for Control of Two-Phase Flows Governed by the Cahn-Hilliard Navier-Stokes System
- Free Energy of a Nonuniform System. I. Interfacial Free Energy
- 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