Higher-order Cahn–Hilliard equations with dynamic boundary conditions
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Alain Miranville | Rosa Maria Mininni | Silvia Romanelli | R. Mininni | A. Miranville | S. Romanelli
[1] Giulio Schimperna,et al. On a Class of Cahn-Hilliard Models with Nonlinear Diffusion , 2011, SIAM J. Math. Anal..
[2] Irena Pawłow,et al. A sixth order Cahn-Hilliard type equation arising in oil-water-surfactant mixtures , 2011 .
[3] R. Chill,et al. Convergence to steady states of solutions of the Cahn-Hilliard equation with dynamic boundary conditions , 2003 .
[4] Gompper,et al. Ginzburg-Landau theory of ternary amphiphilic systems. I. Gaussian interface fluctuations. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[5] Alain Miranville,et al. Sixth-order Cahn–Hilliard equations with singular nonlinear terms , 2015 .
[6] Jie Shen,et al. Efficient energy stable schemes with spectral discretization in space for anisotropic , 2013 .
[7] Peter Galenko,et al. Phase-field-crystal and Swift-Hohenberg equations with fast dynamics. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.
[8] Sergey Zelik,et al. The Cahn-Hilliard Equation with Logarithmic Potentials , 2011 .
[9] I. Pawlow,et al. On a class of sixth order viscous Cahn-Hilliard type equations , 2012 .
[10] Alain Miranville,et al. Sixth‐order Cahn–Hilliard systems with dynamic boundary conditions , 2015 .
[11] Sergey Zelik,et al. Chapter 3 Attractors for Dissipative Partial Differential Equations in Bounded and Unbounded Domains , 2008 .
[12] Ciprian G. Gal,et al. A Cahn–Hilliard model in bounded domains with permeable walls , 2006 .
[13] J. E. Hilliard,et al. Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .
[14] Piotr Rybka,et al. Global Weak Solutions to a Sixth Order Cahn-Hilliard Type Equation , 2012, SIAM J. Math. Anal..
[15] Bernd Rinn,et al. Phase separation in confined geometries: Solving the Cahn–Hilliard equation with generic boundary conditions , 2001 .
[16] Morgan Pierre,et al. A NUMERICAL ANALYSIS OF THE CAHN-HILLIARD EQUATION WITH DYNAMIC BOUNDARY CONDITIONS , 2010 .
[17] P. Voorhees,et al. Faceting of a growing crystal surface by surface diffusion. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.
[18] Piotr Rybka,et al. On a Higher Order Convective Cahn-Hilliard-Type Equation , 2012, SIAM J. Appl. Math..
[19] Alain Miranville,et al. On the phase-field-crystal model with logarithmic nonlinear terms , 2016 .
[20] Madalina Petcu,et al. A numerical analysis of the Cahn–Hilliard equation with non-permeable walls , 2014, Numerische Mathematik.
[21] Gompper,et al. Ginzburg-Landau theory of ternary amphiphilic systems. II. Monte Carlo simulations. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[22] R. Temam. Infinite Dimensional Dynamical Systems in Mechanics and Physics Springer Verlag , 1993 .
[23] H. Löwen,et al. Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview , 2012, 1207.0257.
[24] Alain Miranville,et al. On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions , 2009 .
[25] M. Grant,et al. Diffusive atomistic dynamics of edge dislocations in two dimensions. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.
[26] I. Pawlow,et al. A Cahn-Hilliard equation with singular diffusion , 2012, 1206.5604.
[27] Maurizio Grasselli,et al. Well-posedness and longtime behavior for the modified phase-field crystal equation , 2013 .
[28] F. Otto,et al. Upper Bounds on Coarsening Rates , 2002 .
[29] Cheng Wang,et al. Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation , 2009, J. Comput. Phys..
[30] Philipp Maass,et al. Time-dependent density functional theory and the kinetics of lattice gas systems in contact with a wall , 1998 .
[31] Steven M. Wise,et al. An Energy Stable and Convergent Finite-Difference Scheme for the Modified Phase Field Crystal Equation , 2011, SIAM J. Numer. Anal..
[32] Axel Voigt,et al. A new phase-field model for strongly anisotropic systems , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[33] Philipp Maass,et al. Novel Surface Modes in Spinodal Decomposition , 1997 .
[34] Philipp Maass,et al. Diverging time and length scales of spinodal decomposition modes in thin films , 1998 .
[35] Amy Novick-Cohen,et al. Chapter 4 The Cahn–Hilliard Equation , 2008 .
[36] Sergey Zelik,et al. Exponential attractors for the Cahn–Hilliard equation with dynamic boundary conditions , 2005 .
[37] R. Temam,et al. Navier-Stokes equations: theory and numerical analysis: R. Teman North-Holland, Amsterdam and New York. 1977. 454 pp. US $45.00 , 1978 .
[38] James S. Langer,et al. Theory of spinodal decomposition in alloys , 1971 .
[39] Alain Miranville,et al. Asymptotic behavior of a sixth-order Cahn-Hilliard system , 2013 .
[40] Thomas Wanner,et al. Spinodal Decomposition for the¶Cahn-Hilliard Equation in Higher Dimensions:¶Nonlinear Dynamics , 2000 .
[41] Flore Nabet. Convergence of a finite-volume scheme for the Cahn–Hilliard equation with dynamic boundary conditions , 2016 .
[42] Thomas Wanner,et al. Spinodal Decomposition for the Cahn–Hilliard Equation in Higher Dimensions.¶Part I: Probability and Wavelength Estimate , 1998 .
[43] Alain Miranville,et al. A Cahn-Hilliard model in a domain with non-permeable walls , 2011 .
[44] Joel Berry,et al. Simulation of an atomistic dynamic field theory for monatomic liquids: freezing and glass formation. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.
[45] Stig Larsson,et al. THE CAHN-HILLIARD EQUATION , 2007 .
[46] John W. Cahn,et al. On Spinodal Decomposition , 1961 .
[47] A. Miranville,et al. Higher-order models in phase separation , 2016 .
[48] Jan Prüss,et al. Convergence to steady states of solutions of the Cahn–Hilliard and Caginalp equations with dynamic boundary conditions , 2006 .
[49] Alain Miranville,et al. Long time behavior of the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions , 2010 .
[50] Gunduz Caginalp,et al. Anisotropic phase field equations of arbitrary order , 2010 .
[51] Jan Prüss,et al. Maximal regularity and asymptotic behavior of solutions for the Cahn–Hilliard equation with dynamic boundary conditions , 2006 .
[52] Hao Wu,et al. Robust exponential attractors for the modified phase-field crystal equation , 2013 .
[53] Flore Nabet,et al. An error estimate for a finite-volume scheme for the Cahn–Hilliard equation with dynamic boundary conditions , 2018, Numerische Mathematik.
[54] Sergey Zelik,et al. THE CAHN-HILLIARD EQUATION WITH SINGULAR POTENTIALS AND DYNAMIC BOUNDARY CONDITIONS , 2009, 0904.4023.
[55] Cheng Wang,et al. An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation , 2009, SIAM J. Numer. Anal..
[56] Hao-qing Wu,et al. Convergence to Equilibrium for the Cahn-Hilliard Equation with Wentzell Boundary Condition , 2004, 0705.3362.
[57] P. Gennes. Dynamics of fluctuations and spinodal decomposition in polymer blends , 1980 .