Cahn-Hilliard equation with nonlocal singular free energies

DOI10.1007/s10231-014-0411-9zbMath1320.35083arXiv1311.3642OpenAlexW2075671310MaRDI QIDQ2353830

Maurizio Grasselli, Stefano Bosia, Helmut Abels

Publication date: 9 July 2015

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.3642

zbMATH Keywords

global attractorslogarithmic potentialno-flux boundary conditionregional fractional Laplacian

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Attractors (35B41) Integro-partial differential equations (45K05) Initial-boundary value problems for second-order parabolic equations (35K20) Stefan problems, phase changes, etc. (80A22) Nonlinear evolution equations (47J35) Semilinear parabolic equations (35K58) Integro-partial differential equations (35R09)

Related Items

On an application of Tikhonov's fixed point theorem to a nonlocal Cahn-Hilliard type system modeling phase separation ⋮ Local asymptotics for nonlocal convective Cahn-Hilliard equations with \(W^{1,1}\) kernel and singular potential ⋮ Fractional Cahn-Hilliard, Allen-Cahn and porous medium equations ⋮ Preconditioners with symmetrized techniques for space fractional Cahn-Hilliard equations ⋮ On the nonlocal Cahn-Hilliard equation with nonlocal dynamic boundary condition and boundary penalization ⋮ Degenerate nonlocal Cahn-Hilliard equations: well-posedness, regularity and local asymptotics ⋮ Well-posedness of the Cahn-Hilliard equation with fractional free energy and its Fourier Galerkin approximation ⋮ On the initial value problem for a class of nonlinear biharmonic equation with time-fractional derivative ⋮ The separation property for 2D Cahn-Hilliard equations: local, nonlocal and fractional energy cases ⋮ The robust physics-informed neural networks for a typical fourth-order phase field model ⋮ Finite element simulation and efficient algorithm for fractional Cahn-Hilliard equation ⋮ Doubly nonlocal Cahn-Hilliard equations ⋮ Non-local Cahn–Hilliard equations with fractional dynamic boundary conditions ⋮ Optimal distributed control of a generalized fractional Cahn-Hilliard system ⋮ Cahn-Hilliard equations governed by weakly nonlocal conservation laws and weakly nonlocal particle interactions ⋮ Nonlocal-to-local convergence of Cahn-Hilliard equations: Neumann boundary conditions and viscosity terms ⋮ Nonlocal Phase Field Models of Viscous Cahn–Hilliard Type ⋮ Convergence of solutions for the fractional Cahn-Hilliard system ⋮ Global solutions to a model with Dirichlet boundary conditions for interface motion by interface diffusion ⋮ On the strong-to-strong interaction case for doubly nonlocal Cahn-Hilliard equations ⋮ On a fractional thin film equation ⋮ The nonlocal Cahn-Hilliard equation with singular potential: well-posedness, regularity and strict separation property ⋮ An efficient second-order energy stable BDF scheme for the space fractional Cahn-Hilliard equation ⋮ Analysis and Approximation of a Fractional Cahn--Hilliard Equation ⋮ Existence and energy estimates of weak solutions for nonlocal Cahn-Hilliard equations on an unbounded domain ⋮ Convergence of a nonlocal to a local diffuse interface model for two-phase flow with unmatched densities ⋮ The Cahn-Hilliard equation and some of its variants ⋮ Well-posedness and regularity for a generalized fractional Cahn-Hilliard system

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Longtime behavior of nonlocal Cahn-Hilliard equations
• Regularity and separation from potential barriers for a non-local phase-field system
• Convergence of solutions of a non-local phase-field system
• The Cahn-Hilliard equation with logarithmic potentials
• Sobolev, Besov and Nikolskii fractional spaces: Imbeddings and comparisons for vector valued spaces on an interval
• An analytic approach to purely nonlocal Bellman equations arising in models of stochastic control
• Front-type solutions of fractional Allen-Cahn equation
• On the Cahn-Hilliard equation
• Phase segregation dynamics in particle systems with long range interactions. I: Macroscopic limits
• Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations
• Censored stable processes
• On a nonlocal phase separation model
• The Neumann boundary problem for a nonlocal Cahn-Hilliard equation
• Convergence to equilibrium for the Cahn-Hilliard equation with a logarithmic free energy
• A result on the existence of global attractors for semigroups of closed operators
• The Dirichlet boundary problem for a nonlocal Cahn-Hilliard equation
• Some global dynamical properties of a class of pattern formation equations
• Nonlinear evolution inclusions arising from phase change models
• Phase Segregation Dynamics in Particle Systems with Long Range Interactions II: Interface Motion
• On the Cahn-Hilliard equation with a logarithmic free energy
• On the Cahn–Hilliard Equation with Degenerate Mobility
• Free Energy of a Nonuniform System. I. Interfacial Free Energy