On a Cahn–Hilliard system with convection and dynamic boundary conditions
暂无分享,去创建一个
[1] M. Kubo. The Cahn–Hilliard equation with time-dependent constraint , 2012 .
[2] Jacques Simeon,et al. Compact Sets in the Space L~(O, , 2005 .
[3] 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..
[4] Morton E. Gurtin,et al. Continuum theory of thermally induced phase transitions based on an order parameter , 1993 .
[5] Ciprian G. Gal,et al. A Cahn–Hilliard model in bounded domains with permeable walls , 2006 .
[6] E. Boschi. Recensioni: J. L. Lions - Quelques méthodes de résolution des problémes aux limites non linéaires. Dunod, Gauthier-Vi;;ars, Paris, 1969; , 1971 .
[7] 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 .
[8] J. Simon. Compact sets in the spaceLp(O,T; B) , 1986 .
[9] Songmu Zheng,et al. The Cahn-Hilliard equation with dynamic boundary conditions , 2003, Advances in Differential Equations.
[10] M. Gurtin. Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance , 1996 .
[11] P. Podio-Guidugli. Models of phase segregation and diffusion of atomic species on a lattice , 2006 .
[12] Alain Miranville,et al. Long time behavior of the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions , 2010 .
[13] H. Brezis. Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert , 1973 .
[14] J. Lions. Quelques méthodes de résolution de problèmes aux limites non linéaires , 1969 .
[15] Quan-Fang Wang. Optimal distributed control of nonlinear Cahn–Hilliard systems with computational realization , 2011 .
[16] R. Chill,et al. Convergence to steady states of solutions of the Cahn-Hilliard equation with dynamic boundary conditions , 2003 .
[17] Pierluigi Colli,et al. Equation and dynamic boundary condition of Cahn-Hilliard type with singular potentials , 2015, 1502.05159.
[18] Alain Miranville,et al. On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions , 2009 .
[19] Jan Prüss,et al. Maximal regularity and asymptotic behavior of solutions for the Cahn–Hilliard equation with dynamic boundary conditions , 2006 .
[20] 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 .
[21] C. Gal. Robust exponential attractors for a conserved Cahn-Hilliard model with singularly perturbed boundary conditions , 2008 .
[22] Pierluigi Colli,et al. On the Cahn–Hilliard equation with dynamic boundary conditions and a dominating boundary potential , 2014, 1403.1663.
[23] C. M. Elliott,et al. The viscous Cahn-Hilliard equation , 2002 .
[24] T. Fukao,et al. A Boundary Control Problem for the Equation and Dynamic Boundary Condition of Cahn–Hilliard Type , 2017 .
[25] Alain Miranville,et al. A Cahn-Hilliard model in a domain with non-permeable walls , 2011 .
[26] Jan Prüss,et al. Convergence to steady states of solutions of the Cahn–Hilliard and Caginalp equations with dynamic boundary conditions , 2006 .
[27] J. Sprekels,et al. Second-order analysis of a boundary control problem for the viscous Cahn--Hilliard equation with dynamic boundary condition , 2014, 1410.8443.
[28] P. Colli,et al. Global solution to the Allen–Cahn equation with singular potentials and dynamic boundary conditions , 2012, 1206.6738.
[29] Andrew M. Stuart,et al. The viscous Cahn-Hilliard equation. I. Computations , 1995 .
[30] Jürgen Sprekels,et al. Optimal Control of an Allen-Cahn Equation with Singular Potentials and Dynamic Boundary Condition , 2012, SIAM J. Control. Optim..
[31] Pierluigi Colli,et al. Well-posedness and Long-time Behavior for a Nonstandard Viscous Cahn-Hilliard System , 2011, SIAM J. Appl. Math..
[32] Pierluigi Colli,et al. Cahn-Hilliard equation with dynamic boundary conditions and mass constraint on the boundary , 2014, 1412.1932.
[33] Yifu Wang,et al. Optimal Control Problem for Cahn–Hilliard Equations with State Constraint , 2015 .
[34] Charles M. Elliott,et al. On the Cahn-Hilliard equation , 1986 .
[35] Viorel Barbu,et al. Nonlinear Differential Equations of Monotone Types in Banach Spaces , 2010 .
[36] Andrew M. Stuart,et al. Viscous Cahn–Hilliard Equation II. Analysis , 1996 .
[37] A. Miranville,et al. A Cahn-Hilliard-Gurtin model with dynamic boundary conditions , 2012 .
[38] Jöran Bergh,et al. General Properties of Interpolation Spaces , 1976 .
[39] 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 .
[40] Xiaopeng Zhao,et al. Optimal Control for the Convective Cahn–Hilliard Equation in 2D Case , 2014 .
[41] Jöran Bergh,et al. Interpolation Spaces: An Introduction , 2011 .
[42] Pierluigi Colli,et al. A Boundary Control Problem for the Viscous Cahn–Hilliard Equation with Dynamic Boundary Conditions , 2014, 1407.3916.
[43] Pierluigi Colli,et al. A boundary control problem for the pure Cahn–Hilliard equation with dynamic boundary conditions , 2015, 1503.03213.
[44] Jürgen Sprekels,et al. Optimal Boundary Control of a Viscous Cahn-Hilliard System with Dynamic Boundary Condition and Double Obstacle Potentials , 2014, SIAM J. Control. Optim..
[45] Alain Miranville,et al. A Variational Approach to a Cahn–Hilliard Model in a Domain with Nonpermeable Walls , 2013 .
[46] Madalina Petcu,et al. A numerical analysis of the Cahn–Hilliard equation with non-permeable walls , 2014, Numerische Mathematik.
[47] J. E. Hilliard,et al. Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .
[48] 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..
[49] Michael Hintermüller,et al. Optimal control of a semidiscrete Cahn-Hilliard-Navier-Stokes system , 2012 .
[50] Sergey Zelik,et al. Robust exponential attractors for Cahn‐Hilliard type equations with singular potentials , 2004 .
[51] Hao Wu,et al. Asymptotic behavior of a Cahn-Hilliard equation with Wentzell boundary conditions and mass conservation , 2008 .
[52] Xiaopeng Zhao,et al. Optimal control of the convective Cahn–Hilliard equation , 2013 .
[53] S. Nakagiri,et al. OPTIMAL CONTROL OF DISTRIBUTED PARAMETER SYSTEM GIVEN BY CAHN-HILLIARD EQUATION , 2014 .
[54] Sergey Zelik,et al. The Cahn-Hilliard Equation with Logarithmic Potentials , 2011 .