The viscous Cahn-Hilliard equation: Morse decomposition and structure of the global attractor

DOI10.1090/S0002-9947-99-02445-9zbMath0927.35045MaRDI QIDQ4243607

Amy Novick-Cohen, Michael Grinfeld

Publication date: 19 May 1999

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

connecting orbitsChaffee-Infante equationdimension of the unstable manifoldexplicit energy calculationsnonlocal reaction-diffusion limit

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Initial value problems for higher-order parabolic equations (35K30)

Related Items (38)

Symmetries and solutions to the thin film equations ⋮ Energy levels of steady states for thin-film-type equations ⋮ A conservative nonlinear difference scheme for the viscous Cahn-Hilliard equation ⋮ A high order operator splitting method based on spectral deferred correction for the nonlocal viscous Cahn-Hilliard equation ⋮ A conservative difference scheme for the viscous Cahn--Hilliard equation with a nonconstant gradient energy coefficient ⋮ Long-wave convection in a two-layer system ⋮ Linear, second order and unconditionally energy stable schemes for the viscous Cahn-Hilliard equation with hyperbolic relaxation using the invariant energy quadratization method ⋮ Computer-Assisted Proof of Heteroclinic Connections in the One-Dimensional Ohta--Kawasaki Model ⋮ Error estimates for the scalar auxiliary variable (SAV) schemes to the viscous Cahn-Hilliard equation with hyperbolic relaxation ⋮ Spinodal decomposition and coarsening fronts in the Cahn-Hilliard equation ⋮ Singularly perturbed 1D Cahn-Hilliard equation revisited ⋮ The viscous Cahn-Hilliard equation with inertial term ⋮ Optimal Boundary Control of a Viscous Cahn--Hilliard System with Dynamic Boundary Condition and Double Obstacle Potentials ⋮ STRUCTURE OF THE ATTRACTOR OF THE CAHN–HILLIARD EQUATION ON A SQUARE ⋮ A MATHEMATICAL STUDY OF A BISTABLE NEMATIC LIQUID CRYSTAL DEVICE ⋮ Optimal borel measure-valued controls to the viscous Cahn–Hilliard–Oberbeck–Boussinesq phase-field system on two-dimensional bounded domains ⋮ The viscous Cahn-Hilliard equation with periodic potentials and sources ⋮ A fourth-order parabolic equation modeling epitaxial thin film growth ⋮ Optimal control problem for viscous Cahn-Hilliard equation ⋮ Equilibria with many nuclei for the Cahn-Hilliard equation ⋮ Dynamics of the viscous Cahn-Hilliard equation ⋮ Global solutions and smoothing effects for semi-linear evolution equations in circular domains ⋮ Solutions of fourth-order parabolic equation modeling thin film growth ⋮ On the viscous Allen-Cahn and Cahn-Hilliard systems with Willmore regularization. ⋮ Initial and boundary value problems for a class of nonlinear metaparabolic equations ⋮ Bifurcations in the regularized Ericksen bar model ⋮ Thermodynamics of Elastoplastic Porous Rocks at Large Strains Towards Earthquake Modeling ⋮ Degenerate Nucleation in the Cahn--Hilliard--Cook Model ⋮ Numerical approximation for viscous Cahn–Hilliard equation via septic B-spline ⋮ On the stationary Cahn-Hilliard equation: Interior spike solutions ⋮ Bifurcations of steady states for the Eguchi–Oki–Matsumura model of phase separation ⋮ Stationary Solutions for the Cahn — Hilliard Equation Coupled with Neumann Boundary Conditions ⋮ Metastability in chemotaxis models ⋮ Blow-up phenomena for a class of metaparabolic equations with time dependent coeffcient ⋮ Weak and very weak solutions to the viscous Cahn-Hilliard-Oberbeck-Boussinesq phase-field system on two-dimensional bounded domains ⋮ On the existence of global attractor for 3D viscous Cahn-Hilliard equation ⋮ Asymptotic behaviour of the viscous Cahn-Hilliard equation ⋮ Convergence of solutions to cahn-hilliard equation

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