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A stabilizing effect of a high-frequency driving force on the motion of a viscous, compressible, and heat conducting fluid
Robust exponential attractors and convergence to equilibria for non-isothermal Cahn-Hilliard equations with dynamic boundary conditions
1. | Department of Mathematics, University of Missouri, Columbia, MO, 65211, United States |
2. | Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 6086, SP2MI, 86962 Chasseneuil Futuroscope Cedex |
[1] |
Cecilia Cavaterra, Maurizio Grasselli, Hao Wu. Non-isothermal viscous Cahn-Hilliard equation with inertial term and dynamic boundary conditions. Communications on Pure and Applied Analysis, 2014, 13 (5) : 1855-1890. doi: 10.3934/cpaa.2014.13.1855 |
[2] |
Ciprian G. Gal, Maurizio Grasselli. Singular limit of viscous Cahn-Hilliard equations with memory and dynamic boundary conditions. Discrete and Continuous Dynamical Systems - B, 2013, 18 (6) : 1581-1610. doi: 10.3934/dcdsb.2013.18.1581 |
[3] |
Ciprian G. Gal. Robust exponential attractors for a conserved Cahn-Hilliard model with singularly perturbed boundary conditions. Communications on Pure and Applied Analysis, 2008, 7 (4) : 819-836. doi: 10.3934/cpaa.2008.7.819 |
[4] |
Laurence Cherfils, Madalina Petcu. On the viscous Cahn-Hilliard-Navier-Stokes equations with dynamic boundary conditions. Communications on Pure and Applied Analysis, 2016, 15 (4) : 1419-1449. doi: 10.3934/cpaa.2016.15.1419 |
[5] |
Irena Pawłow, Wojciech M. Zajączkowski. On a class of sixth order viscous Cahn-Hilliard type equations. Discrete and Continuous Dynamical Systems - S, 2013, 6 (2) : 517-546. doi: 10.3934/dcdss.2013.6.517 |
[6] |
Riccarda Rossi. On two classes of generalized viscous Cahn-Hilliard equations. Communications on Pure and Applied Analysis, 2005, 4 (2) : 405-430. doi: 10.3934/cpaa.2005.4.405 |
[7] |
Jan Prüss, Vicente Vergara, Rico Zacher. Well-posedness and long-time behaviour for the non-isothermal Cahn-Hilliard equation with memory. Discrete and Continuous Dynamical Systems, 2010, 26 (2) : 625-647. doi: 10.3934/dcds.2010.26.625 |
[8] |
Erica Ipocoana, Andrea Zafferi. Further regularity and uniqueness results for a non-isothermal Cahn-Hilliard equation. Communications on Pure and Applied Analysis, 2021, 20 (2) : 763-782. doi: 10.3934/cpaa.2020289 |
[9] |
Desheng Li, Xuewei Ju. On dynamical behavior of viscous Cahn-Hilliard equation. Discrete and Continuous Dynamical Systems, 2012, 32 (6) : 2207-2221. doi: 10.3934/dcds.2012.32.2207 |
[10] |
Alain Miranville, Sergey Zelik. The Cahn-Hilliard equation with singular potentials and dynamic boundary conditions. Discrete and Continuous Dynamical Systems, 2010, 28 (1) : 275-310. doi: 10.3934/dcds.2010.28.275 |
[11] |
Laurence Cherfils, Madalina Petcu, Morgan Pierre. A numerical analysis of the Cahn-Hilliard equation with dynamic boundary conditions. Discrete and Continuous Dynamical Systems, 2010, 27 (4) : 1511-1533. doi: 10.3934/dcds.2010.27.1511 |
[12] |
Gianni Gilardi, A. Miranville, Giulio Schimperna. On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions. Communications on Pure and Applied Analysis, 2009, 8 (3) : 881-912. doi: 10.3934/cpaa.2009.8.881 |
[13] |
Ciprian G. Gal, Maurizio Grasselli. The non-isothermal Allen-Cahn equation with dynamic boundary conditions. Discrete and Continuous Dynamical Systems, 2008, 22 (4) : 1009-1040. doi: 10.3934/dcds.2008.22.1009 |
[14] |
Ciprian G. Gal, Maurizio Grasselli. Longtime behavior of nonlocal Cahn-Hilliard equations. Discrete and Continuous Dynamical Systems, 2014, 34 (1) : 145-179. doi: 10.3934/dcds.2014.34.145 |
[15] |
Alain Miranville. Existence of solutions for Cahn-Hilliard type equations. Conference Publications, 2003, 2003 (Special) : 630-637. doi: 10.3934/proc.2003.2003.630 |
[16] |
Matthieu Brachet, Philippe Parnaudeau, Morgan Pierre. Convergence to equilibrium for time and space discretizations of the Cahn-Hilliard equation. Discrete and Continuous Dynamical Systems - S, 2022, 15 (8) : 1987-2031. doi: 10.3934/dcdss.2022110 |
[17] |
Anna Kostianko, Sergey Zelik. Inertial manifolds for the 3D Cahn-Hilliard equations with periodic boundary conditions. Communications on Pure and Applied Analysis, 2015, 14 (5) : 2069-2094. doi: 10.3934/cpaa.2015.14.2069 |
[18] |
Christopher P. Grant. Grain sizes in the discrete Allen-Cahn and Cahn-Hilliard equations. Discrete and Continuous Dynamical Systems, 2001, 7 (1) : 127-146. doi: 10.3934/dcds.2001.7.127 |
[19] |
Jie Shen, Xiaofeng Yang. Numerical approximations of Allen-Cahn and Cahn-Hilliard equations. Discrete and Continuous Dynamical Systems, 2010, 28 (4) : 1669-1691. doi: 10.3934/dcds.2010.28.1669 |
[20] |
Alain Miranville, Wafa Saoud, Raafat Talhouk. On the Cahn-Hilliard/Allen-Cahn equations with singular potentials. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 3633-3651. doi: 10.3934/dcdsb.2018308 |
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