A Boundary Control Problem for the Viscous Cahn–Hilliard Equation with Dynamic Boundary Conditions
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[1] Jürgen Sprekels,et al. Optimal Control of an Allen-Cahn Equation with Singular Potentials and Dynamic Boundary Condition , 2012, SIAM J. Control. Optim..
[2] Xiaopeng Zhao,et al. Optimal control of the convective Cahn–Hilliard equation , 2013 .
[3] J. Lions,et al. Non-homogeneous boundary value problems and applications , 1972 .
[4] R. Chill,et al. Convergence to steady states of solutions of the Cahn-Hilliard equation with dynamic boundary conditions , 2003 .
[5] Pierluigi Colli,et al. On the Cahn–Hilliard equation with dynamic boundary conditions and a dominating boundary potential , 2014, 1403.1663.
[6] Jan Prüss,et al. Convergence to steady states of solutions of the Cahn–Hilliard and Caginalp equations with dynamic boundary conditions , 2006 .
[7] Jacques Simeon,et al. Compact Sets in the Space L~(O, , 2005 .
[8] Jürgen Sprekels,et al. Optimal Distributed Control of a Nonlocal Convective Cahn-Hilliard Equation by the Velocity in Three Dimensions , 2015, SIAM J. Control. Optim..
[9] Michael Hintermüller,et al. Optimal control of a semidiscrete Cahn-Hilliard-Navier-Stokes system , 2012 .
[10] Sulle equazioni differenziali astratte lineari del primo e del secondo ordine negli spazi di Hilbert , 1967 .
[11] Jürgen Sprekels,et al. Distributed optimal control of a nonstandard system of phase field equations , 2011, Continuum Mechanics and Thermodynamics.
[12] Michael Hintermüller,et al. Distributed Optimal Control of the Cahn-Hilliard System Including the Case of a Double-Obstacle Homogeneous Free Energy Density , 2012, SIAM J. Control. Optim..
[13] Sergey Zelik,et al. Robust exponential attractors for Cahn‐Hilliard type equations with singular potentials , 2004 .
[14] H. Israel,et al. Long time behavior of an Allen-Cahn type equation with a singular potential and dynamic boundary conditions , 2012 .
[15] E. Rocca,et al. Optimal distributed control of a nonlocal convective Cahn-Hilliard equation by the velocity in 3D , 2014, 1404.1765.
[16] P. Colli,et al. Global solution to the Allen–Cahn equation with singular potentials and dynamic boundary conditions , 2012, 1206.6738.
[17] Alain Miranville,et al. On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions , 2009 .
[18] J. Lions,et al. Équations Différentielles Opérationnelles Et Problèmes Aux Limites , 1961 .
[19] J. E. Hilliard,et al. Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .
[20] J. Sprekels,et al. A Deep Quench Approach to the Optimal Control of an Allen–Cahn Equation with Dynamic Boundary Conditions and Double Obstacles , 2013 .
[21] Pierluigi Colli,et al. The Allen–Cahn equation with dynamic boundary conditions and mass constraints , 2014, 1405.0116.
[22] S. Nakagiri,et al. OPTIMAL CONTROL OF DISTRIBUTED PARAMETER SYSTEM GIVEN BY CAHN-HILLIARD EQUATION , 2014 .
[23] J. Simon. Compact sets in the spaceLp(O,T; B) , 1986 .
[24] Charles M. Elliott,et al. On the Cahn-Hilliard equation , 1986 .
[25] Andrew M. Stuart,et al. Viscous Cahn–Hilliard Equation II. Analysis , 1996 .
[26] Songmu Zheng,et al. The Cahn-Hilliard equation with dynamic boundary conditions , 2003, Advances in Differential Equations.
[27] P. Colli,et al. Analysis and Optimal Boundary Control of a Nonstandard System of Phase Field Equations , 2012, 1201.5541.
[28] Jan Prüss,et al. Maximal regularity and asymptotic behavior of solutions for the Cahn–Hilliard equation with dynamic boundary conditions , 2006 .
[29] J. E. Hilliard,et al. Free Energy of a Nonuniform System. I. Interfacial Free Energy and Free Energy of a Nonuniform System. III. Nucleation in a Two‐Component Incompressible Fluid , 2013 .
[30] P. Podio-Guidugli. Models of phase segregation and diffusion of atomic species on a lattice , 2006 .
[31] F. Rühs,et al. J. L. Lions, Équations Différentielles Opérationnelles et Problèmes aux Limites. IX + 292 S. Berlin/Göttingen/Heidelberg 1961. Springer-Verlag. Preis geb. 64,— , 1962 .
[32] Christian Kahle,et al. A Nonlinear Model Predictive Concept for Control of Two-Phase Flows Governed by the Cahn-Hilliard Navier-Stokes System , 2011, System Modelling and Optimization.
[33] Stig Larsson,et al. THE CAHN-HILLIARD EQUATION , 2007 .
[34] Nermina Mujaković,et al. The existence of a global solution for one dimensional compressible viscous micropolar fluid with non-homogeneous boundary conditions for temperature , 2014 .
[35] Xiaopeng Zhao,et al. Optimal Control for the Convective Cahn–Hilliard Equation in 2D Case , 2014 .
[36] Hao-qing Wu,et al. Convergence to Equilibrium for the Cahn-Hilliard Equation with Wentzell Boundary Condition , 2004, 0705.3362.