On the complex version of the Cahn–Hilliard–Oono type equation for long interactions phase separation
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References
- Cahn J.W., Hilliard J.E., Free energy of a nonuniform system I. Interfacial free energy, The Journal of Chemical Physics, 28, 258–267, 1958.
- Cahn J.W., Hilliard J.E., Spinodal decomposition: A reprise, Acta Metallurgica, 19, 151–161, 1971.
- Cahn J.W., Hilliard J.E., Surface motion by surface diffusion, Acta Metallurgica, 42, 1045–1063, 1994.
- Cahn J.W., Hilliard J.E., Linking anisotropic and diffusive surface motion laws via gradient flows, Journal of Statistical Physics, 77, 183–197, 1994.
- Novick-Cohen A., Segel L.A., Nonlinear aspects of the Cahn–Hilliard equation, Physica D: Nonlinear Phenomena, 10(3), 277–298, 1984.
- Miranville A., The Cahn–Hilliard equation and some of its variants, AIMS Mathematics, 2(3), 479–544, 2017.
- Oono Y., Puri S., Computationally efficient modeling of ordering of quenched phases, Physical Review Letters, 58, 836–839, 1987.
- Villain-Guillot S., Phases modulées et dynamique de Cahn–Hilliard, Habilitation Thesis, Physique [physics]. Université Sciences et Technologies, Bordeaux I, 2010.
- Aristotelous A.C., Karakashian O.A., Wise S.M., Adaptive second-order in time primitive-variable discontinuous Galerkin schemes for a Cahn–Hilliard equation with a mass source, IMA Journal of Numerical Analysis, 35(3), 1167–1198, 2015.
- Cherfils L., Fakih H., Miranville A., Finite-dimensional attractors for the Bertozzi–Esedoglu–Gillette–Cahn–Hilliard equation in image inpainting, Inverse Problems and Imaging, 9(1), 105–125, 2015.
- Cherfils L., Fakih H., Miranville A., On the Bertozzi–Esedoglu–Gillette–Cahn–Hilliard equation with logarithmic nonlinear terms, SIAM Journal on Imaging Sciences, 8(2), 1123–1140, 2015.
- Cherfils L., Fakih H., Miranville A., A Cahn–Hilliard system with a fidelity term for color image inpainting, Journal of Mathematical Imaging and Vision, 54, 117–131, 2016.
- Cherfils L., Miranville A., Zelik S., On a generalized Cahn–Hilliard equation with biological applications, Discrete and Continuous Dynamical Systems - Series B, 19(7), 2013–2026, 2014.
- Cherfils L., Petcu M., Pierre M., A numerical analysis of the Cahn–Hilliard equation with dynamic boundary conditions, Discrete and Continuous Dynamical Systems, 27(4), 1511–1533, 2010.
- Elliott C.M., French D.A., Milner F.A., A second order splitting method for the Cahn–Hilliard equation, Numerische Mathematik, 54, 575–590, 1989.
- Fakih H., Asymptotic behavior of a generalized Cahn–Hilliard equation with a mass source, Applicable Analysis, 96(2), 324–348, 2017.
- Fakih H., A Cahn–Hilliard equation with a proliferation term for biological and chemical applications, Asymptotic Analysis, 94(1–2), 71–104, 2015.
- Fakih H., Mghames R., Nasreddine N., On the Cahn-Hilliard equation with mass source for biological applications, Communications on Pure and Applied Analysis, 20(2), 495–510, 2021.
- Cherfils L., Fakih H., Grasselli M., Miranville A., A convergent convex splitting scheme for a nonlocal Cahn-Hilliard-Oono thype equation with a transport term, ESAIM: Mathematical Modelling and Numerical Analysis, 55, 225–250, 2021.
- Khain E., Sander L.M., A generalized Cahn–Hilliard equation for biological applications, Physical Review E, 77, 51–129, 2008.
- Miranville A., Asymptotic behavior of the Cahn–Hilliard–Oono equation, Journal of Applied Analysis and Computation, 1(4), 523–536, 2011.
- Miranville A., Asymptotic behavior of a generalized Cahn–Hilliard equation with a proliferation term, Applicable Analysis An International Journal, 92(6), 1308–1321, 2013.
- Miranville A., Existence of solutions to a Cahn–Hilliard type equation with a logarithmic nonlinear term, Mediterranean Journal of Mathematics, 16(6), 1–18, 2019.
- Ern A., Guermond J.L., Éléments Finis: Théorie, Applications, Mise en Oeuvre, Springer, Berlin, 2002.
- Cherfils L., Fakih H., Miranville A., A complex version of the Cahn-Hilliard equation for grayscale image inpainting, Multiscale Modeling Simulation, 15(1), 575–605, 2017.
- Conti M., Gatti S., Miranville A., Multi-component Cahn-Hilliard systems with dynamic boundary conditions, Nonlinear Analysis: Real World Applications, 25, 137–166, 2015.
DOI: https://doi.org/10.2478/ijmce-2024-0018 | Journal eISSN: 2956-7068
Language: English
Page range: 233 - 250
Submitted on: Aug 18, 2023
Accepted on: Nov 16, 2023
Published on: Jan 10, 2024
Published by: Harran University
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year
Keywords:
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© 2024 Hussein Fakih, Mahdi Faour, Wafa Saoud, Yahia Awad, published by Harran University
This work is licensed under the Creative Commons Attribution 4.0 License.