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Cauchy problem for a class of nondiagonalizable hyperbolic systems
A long-time stable fully discrete approximation of the Cahn-Hilliard equation with inertial term
1. | Dipartimento di Matematica, Politecnico di Milano, 20133 Milano |
2. | Groupe de Physique de Matériaux UMR CNRS6634, Université de Rouen, 1, Avenue de l'Université, 76801 Saint-Etienne du Rouvray, France |
3. | Laboratoire de Mathématiques et Applications UMR CNRS 6086, Université de Poitiers, Téléport 2 - BP 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil |
[1] |
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 and Applied Analysis, 2022, 21 (2) : 355-392. doi: 10.3934/cpaa.2021181 |
[2] |
Maurizio Grasselli, Morgan Pierre. Convergence to equilibrium of solutions of the backward Euler scheme for asymptotically autonomous second-order gradient-like systems. Communications on Pure and Applied Analysis, 2012, 11 (6) : 2393-2416. doi: 10.3934/cpaa.2012.11.2393 |
[3] |
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 |
[4] |
Andreas C. Aristotelous, Ohannes Karakashian, Steven M. Wise. A mixed discontinuous Galerkin, convex splitting scheme for a modified Cahn-Hilliard equation and an efficient nonlinear multigrid solver. Discrete and Continuous Dynamical Systems - B, 2013, 18 (9) : 2211-2238. doi: 10.3934/dcdsb.2013.18.2211 |
[5] |
Cristina Pocci. On singular limit of a nonlinear $p$-order equation related to Cahn-Hilliard and Allen-Cahn evolutions. Evolution Equations and Control Theory, 2013, 2 (3) : 517-530. doi: 10.3934/eect.2013.2.517 |
[6] |
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 |
[7] |
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 |
[8] |
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 |
[9] |
Laurence Cherfils, Alain Miranville, Sergey Zelik. On a generalized Cahn-Hilliard equation with biological applications. Discrete and Continuous Dynamical Systems - B, 2014, 19 (7) : 2013-2026. doi: 10.3934/dcdsb.2014.19.2013 |
[10] |
Álvaro Hernández, Michał Kowalczyk. Rotationally symmetric solutions to the Cahn-Hilliard equation. Discrete and Continuous Dynamical Systems, 2017, 37 (2) : 801-827. doi: 10.3934/dcds.2017033 |
[11] |
Fausto Cavalli, Giovanni Naldi. A Wasserstein approach to the numerical solution of the one-dimensional Cahn-Hilliard equation. Kinetic and Related Models, 2010, 3 (1) : 123-142. doi: 10.3934/krm.2010.3.123 |
[12] |
Paola F. Antonietti, Simone Scacchi, Giuseppe Vacca, Marco Verani. $ C^1 $-VEM for some variants of the Cahn-Hilliard equation: A numerical exploration. Discrete and Continuous Dynamical Systems - S, 2022, 15 (8) : 1919-1939. doi: 10.3934/dcdss.2022038 |
[13] |
Nguyen Huy Tuan. Existence and limit problem for fractional fourth order subdiffusion equation and Cahn-Hilliard equation. Discrete and Continuous Dynamical Systems - S, 2021, 14 (12) : 4551-4574. doi: 10.3934/dcdss.2021113 |
[14] |
Aibo Liu, Changchun Liu. Cauchy problem for a sixth order Cahn-Hilliard type equation with inertial term. Evolution Equations and Control Theory, 2015, 4 (3) : 315-324. doi: 10.3934/eect.2015.4.315 |
[15] |
Irena Pawłow, Wojciech M. Zajączkowski. A sixth order Cahn-Hilliard type equation arising in oil-water-surfactant mixtures. Communications on Pure and Applied Analysis, 2011, 10 (6) : 1823-1847. doi: 10.3934/cpaa.2011.10.1823 |
[16] |
Irena Pawłow, Wojciech M. Zajączkowski. The global solvability of a sixth order Cahn-Hilliard type equation via the Bäcklund transformation. Communications on Pure and Applied Analysis, 2014, 13 (2) : 859-880. doi: 10.3934/cpaa.2014.13.859 |
[17] |
Georgia Karali, Yuko Nagase. On the existence of solution for a Cahn-Hilliard/Allen-Cahn equation. Discrete and Continuous Dynamical Systems - S, 2014, 7 (1) : 127-137. doi: 10.3934/dcdss.2014.7.127 |
[18] |
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 |
[19] |
Tomáš Roubíček. Cahn-Hilliard equation with capillarity in actual deforming configurations. Discrete and Continuous Dynamical Systems - S, 2021, 14 (1) : 41-55. doi: 10.3934/dcdss.2020303 |
[20] |
Dimitra Antonopoulou, Georgia Karali, Georgios T. Kossioris. Asymptotics for a generalized Cahn-Hilliard equation with forcing terms. Discrete and Continuous Dynamical Systems, 2011, 30 (4) : 1037-1054. doi: 10.3934/dcds.2011.30.1037 |
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