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On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions
| 1. | Dipartimento di Matematica "F. Casorati", Università di Pavia, Via Ferrata 1, 27100 Pavia |
| 2. | Laboratoire d'Applications des Mathématiques - SP2MI, Boulevard Marie et Pierre Curie - Téléport 2, Chasseneuil Futuroscope Cedex |
| 3. | Dipartimento di Matematica "F.Casorati", Università di Pavia, Via Ferrata, 1, I-27100 Pavia |
| [1] |
Alain Miranville, Sergey Zelik. The Cahn-Hilliard equation with singular potentials and dynamic boundary conditions. Discrete & Continuous Dynamical Systems, 2010, 28 (1) : 275-310. doi: 10.3934/dcds.2010.28.275 |
| [2] |
Laurence Cherfils, Madalina Petcu, Morgan Pierre. A numerical analysis of the Cahn-Hilliard equation with dynamic boundary conditions. Discrete & Continuous Dynamical Systems, 2010, 27 (4) : 1511-1533. doi: 10.3934/dcds.2010.27.1511 |
| [3] |
Cecilia Cavaterra, Maurizio Grasselli, Hao Wu. Non-isothermal viscous Cahn-Hilliard equation with inertial term and dynamic boundary conditions. Communications on Pure & Applied Analysis, 2014, 13 (5) : 1855-1890. doi: 10.3934/cpaa.2014.13.1855 |
| [4] |
Takeshi Fukao, Shuji Yoshikawa, Saori Wada. Structure-preserving finite difference schemes for the Cahn-Hilliard equation with dynamic boundary conditions in the one-dimensional case. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1915-1938. doi: 10.3934/cpaa.2017093 |
| [5] |
Sergey P. Degtyarev. On Fourier multipliers in function spaces with partial Hölder condition and their application to the linearized Cahn-Hilliard equation with dynamic boundary conditions. Evolution Equations & Control Theory, 2015, 4 (4) : 391-429. doi: 10.3934/eect.2015.4.391 |
| [6] |
Ciprian G. Gal, Alain Miranville. Robust exponential attractors and convergence to equilibria for non-isothermal Cahn-Hilliard equations with dynamic boundary conditions. Discrete & Continuous Dynamical Systems - S, 2009, 2 (1) : 113-147. doi: 10.3934/dcdss.2009.2.113 |
| [7] |
Ciprian G. Gal, Maurizio Grasselli. Singular limit of viscous Cahn-Hilliard equations with memory and dynamic boundary conditions. Discrete & Continuous Dynamical Systems - B, 2013, 18 (6) : 1581-1610. doi: 10.3934/dcdsb.2013.18.1581 |
| [8] |
Sergey Zelik, Jon Pennant. Global well-posedness in uniformly local spaces for the Cahn-Hilliard equation in $\mathbb{R}^3$. Communications on Pure & Applied Analysis, 2013, 12 (1) : 461-480. doi: 10.3934/cpaa.2013.12.461 |
| [9] |
Jan Prüss, Vicente Vergara, Rico Zacher. Well-posedness and long-time behaviour for the non-isothermal Cahn-Hilliard equation with memory. Discrete & Continuous Dynamical Systems, 2010, 26 (2) : 625-647. doi: 10.3934/dcds.2010.26.625 |
| [10] |
Makoto Okumura, Takeshi Fukao, Daisuke Furihata, Shuji Yoshikawa. A second-order accurate structure-preserving scheme for the Cahn-Hilliard equation with a dynamic boundary condition. Communications on Pure & Applied Analysis, 2022, 21 (2) : 355-392. doi: 10.3934/cpaa.2021181 |
| [11] |
Dong Li. A regularization-free approach to the Cahn-Hilliard equation with logarithmic potentials. Discrete & Continuous Dynamical Systems, 2022 doi: 10.3934/dcds.2021198 |
| [12] |
Ciprian G. Gal, Hao Wu. Asymptotic behavior of a Cahn-Hilliard equation with Wentzell boundary conditions and mass conservation. Discrete & Continuous Dynamical Systems, 2008, 22 (4) : 1041-1063. doi: 10.3934/dcds.2008.22.1041 |
| [13] |
Gisèle Ruiz Goldstein, Alain Miranville. A Cahn-Hilliard-Gurtin model with dynamic boundary conditions. Discrete & Continuous Dynamical Systems - S, 2013, 6 (2) : 387-400. doi: 10.3934/dcdss.2013.6.387 |
| [14] |
Laurence Cherfils, Madalina Petcu. On the viscous Cahn-Hilliard-Navier-Stokes equations with dynamic boundary conditions. Communications on Pure & Applied Analysis, 2016, 15 (4) : 1419-1449. doi: 10.3934/cpaa.2016.15.1419 |
| [15] |
Alain Miranville, Wafa Saoud, Raafat Talhouk. On the Cahn-Hilliard/Allen-Cahn equations with singular potentials. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 3633-3651. doi: 10.3934/dcdsb.2018308 |
| [16] |
Ciprian G. Gal. Robust exponential attractors for a conserved Cahn-Hilliard model with singularly perturbed boundary conditions. Communications on Pure & Applied Analysis, 2008, 7 (4) : 819-836. doi: 10.3934/cpaa.2008.7.819 |
| [17] |
Anna Kostianko, Sergey Zelik. Inertial manifolds for the 3D Cahn-Hilliard equations with periodic boundary conditions. Communications on Pure & Applied Analysis, 2015, 14 (5) : 2069-2094. doi: 10.3934/cpaa.2015.14.2069 |
| [18] |
Desheng Li, Xuewei Ju. On dynamical behavior of viscous Cahn-Hilliard equation. Discrete & Continuous Dynamical Systems, 2012, 32 (6) : 2207-2221. doi: 10.3934/dcds.2012.32.2207 |
| [19] |
Laurence Cherfils, Alain Miranville, Sergey Zelik. On a generalized Cahn-Hilliard equation with biological applications. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 2013-2026. doi: 10.3934/dcdsb.2014.19.2013 |
| [20] |
Álvaro Hernández, Michał Kowalczyk. Rotationally symmetric solutions to the Cahn-Hilliard equation. Discrete & Continuous Dynamical Systems, 2017, 37 (2) : 801-827. doi: 10.3934/dcds.2017033 |
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