Long time behavior of a singular perturbation of the viscous Cahn–Hilliard–Gurtin equation

DOI10.1002/mma.938zbMath1145.35011OpenAlexW2014686036MaRDI QIDQ5451429

Maurizio Grasselli, Alain Miranville, Ahmed Bonfoh

Publication date: 27 March 2008

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.938

zbMATH Keywords

inertial manifoldsexponential attractorsconvergence to stationary states

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Attractors (35B41) Singular perturbations in context of PDEs (35B25) Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems (37L25)

Related Items (14)

Singularly perturbed 1D Cahn-Hilliard equation revisited ⋮ The viscous Cahn-Hilliard equation with inertial term ⋮ The Cahn-Hilliard/Allen-Cahn equation with inertial and proliferation terms ⋮ A family of structure-preserving exponential time differencing Runge-Kutta schemes for the viscous Cahn-Hilliard equation ⋮ The singular limit dynamics of the phase-field equations ⋮ Long‐time dynamics of the 2D nonisothermal hyperbolic Cahn–Hilliard equations ⋮ The Cahn-Hilliard equation with logarithmic potentials ⋮ Non-isothermal viscous Cahn-Hilliard equation with inertial term and dynamic boundary conditions ⋮ Existence and continuity of inertial manifolds for the hyperbolic relaxation of the viscous Cahn-Hilliard equation ⋮ Global attractors for the 2D hyperbolic Cahn-Hilliard equations ⋮ Global attractors for the semilinear beam equation with localized viscosity ⋮ On the 2D Cahn–Hilliard Equation with Inertial Term ⋮ On the viscous Cahn-Hilliard equation with singular potential and inertial term ⋮ The Cahn-Hilliard equation and some of its variants

Cites Work

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• A descent method for the free energy of multicomponent systems
• Invariant manifolds of nonlinear operators
• Existence and continuity of uniform exponential attractors of the singularity perturbed Hodgkin-Huxley system
• Lower Semicontinuity of a Non-Hyperbolic Attractor
• ON THE HYPERBOLIC RELAXATION OF THE CAHN–HILLIARD EQUATION IN 3D: APPROXIMATION AND LONG TIME BEHAVIOUR

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