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Applicable Analysis
An International Journal
Volume 23, 1986 - Issue 3
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Original Articles

Asymptotic behavior of solution to the Cahn-Hillard equation

Zheng Songmu Department of Mathematics, Purdue University, West Lafayette, 47907, U.S.A
Pages 165-184 | Received 13 Jun 1986, Published online: 02 May 2007

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Xiaopeng Zhao & Changchun Liu. (2013) Optimal control of the convective Cahn–Hilliard equation. Applicable Analysis 92:5, pages 1028-1045.
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Xiaopeng Zhao & Changchun Liu. (2013) The existence of global attractor for a fourth-order parabolic equation. Applicable Analysis 92:1, pages 44-59.
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Maurizio Grasselli, Alain Miranville, Riccarda Rossi & Giulio Schimperna. (2011) Analysis of the Cahn–Hilliard Equation with a Chemical Potential Dependent Mobility. Communications in Partial Differential Equations 36:7, pages 1193-1238.
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Naoyuki Ishimura, Ken-Ichi Nakamura & Masaaki Nakamura. (2006) Bifurcations of steady states for the Eguchi–Oki–Matsumura model of phase separation. Applicable Analysis 85:6-7, pages 831-843.
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Piotr Rybka & Karl-Heinz Hoffnlann. (1999) Convergence of solutions to cahn-hilliard equation. Communications in Partial Differential Equations 24:5-6, pages 1055-1077.
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Articles from other publishers (64)

Stefan Metzger. (2023) A convergent SAV scheme for Cahn–Hilliard equations with dynamic boundary conditions. IMA Journal of Numerical Analysis 43:6, pages 3593-3627.
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Harald Garcke, Patrik Knopf & Sema Yayla. (2022) Long-time dynamics of the Cahn–Hilliard equation with kinetic rate dependent dynamic boundary conditions. Nonlinear Analysis 215, pages 112619.
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Hao Wu. (2022) A review on the Cahn–Hilliard equation: classical results and recent advances in dynamic boundary conditions. Electronic Research Archive 30:8, pages 2788-2832.
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Matthieu Brachet, Philippe Parnaudeau & Morgan Pierre. (2022) Convergence to equilibrium for time and space discretizations of the Cahn-Hilliard equation. Discrete and Continuous Dynamical Systems - S 15:8, pages 1987.
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Wansheng Wang, Zheng Wang & Zhaoxiang Li. (2021) Long time stability of a classical scheme for Cahn-Hilliard equation with polynomial nonlinearity . Applied Numerical Mathematics 165, pages 35-55.
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Pierluigi Colli, Gianni Gilardi & Jürgen Sprekels. (2021) An asymptotic analysis for a generalized Cahn–Hilliard system with fractional operators. Journal of Evolution Equations 21:2, pages 2749-2778.
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Patrik Knopf & Andrea Signori. (2021) On the nonlocal Cahn–Hilliard equation with nonlocal dynamic boundary condition and boundary penalization. Journal of Differential Equations 280, pages 236-291.
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Raffaele Folino, Corrado Lattanzio & Corrado Mascia. (2019) Metastability and Layer Dynamics for the Hyperbolic Relaxation of the Cahn–Hilliard Equation. Journal of Dynamics and Differential Equations 33:1, pages 75-110.
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BENOÎT PERTHAME & ALEXANDRE POULAIN. (2020) Relaxation of the Cahn–Hilliard equation with singular single-well potential and degenerate mobility. European Journal of Applied Mathematics 32:1, pages 89-112.
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Stefan Metzger. (2021) An Efficient and Convergent Finite Element Scheme for Cahn--Hilliard Equations with Dynamic Boundary Conditions. SIAM Journal on Numerical Analysis 59:1, pages 219-248.
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Patrik Knopf, Kei Fong Lam, Chun Liu & Stefan Metzger. (2021) Phase-field dynamics with transfer of materials: The Cahn–Hilliard equation with reaction rate dependent dynamic boundary conditions. ESAIM: Mathematical Modelling and Numerical Analysis 55:1, pages 229-282.
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Patricio Guzmán. (2018) Local Exact Controllability to the Trajectories of the Cahn–Hilliard Equation. Applied Mathematics & Optimization 82:1, pages 279-306.
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Harald Garcke & Patrik Knopf. (2020) Weak Solutions of the Cahn--Hilliard System with Dynamic Boundary Conditions: A Gradient Flow Approach. SIAM Journal on Mathematical Analysis 52:1, pages 340-369.
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Chun Liu & Hao Wu. (2019) An Energetic Variational Approach for the Cahn–Hilliard Equation with Dynamic Boundary Condition: Model Derivation and Mathematical Analysis. Archive for Rational Mechanics and Analysis 233:1, pages 167-247.
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Raffaele Folino, Corrado Lattanzio & Corrado Mascia. (2019) Slow dynamics for the hyperbolic Cahn‐Hilliard equation in one‐space dimension. Mathematical Methods in the Applied Sciences 42:8, pages 2492-2512.
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Gianni Gilardi & Jürgen Sprekels. (2019) Asymptotic limits and optimal control for the Cahn–Hilliard system with convection and dynamic boundary conditions. Nonlinear Analysis 178, pages 1-31.
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Alain Miranville. (2017) The Cahn–Hilliard equation and some of its variants. AIMS Mathematics 2:3, pages 479-544.
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Yifu Wang & Jiashan Zheng. (2016) Periodic solutions to the Cahn-Hilliard equation with constraint. Mathematical Methods in the Applied Sciences 39:4, pages 649-660.
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Jiashan Zheng & Yifu Wang. (2015) Periodic solutions of non-isothermal phase separation models with constraint. Journal of Mathematical Analysis and Applications 432:2, pages 1018-1038.
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Shimin Chai & Yongkui Zou. (2012) The Spectral Method for the Cahn-Hilliard Equation with Concentration-Dependent Mobility. Journal of Applied Mathematics 2012, pages 1-35.
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