Global dynamics of boundary droplets
From MaRDI portal
Publication:379685
DOI10.3934/dcds.2014.34.1zbMath1315.37049OpenAlexW2328763369MaRDI QIDQ379685
Publication date: 11 November 2013
Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/dcds.2014.34.1
global dynamicsinfinite-dimensional dynamical systemsinvariant manifold theorybubble solutionmass-conserving Allen-Cahn equation
Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Invariant manifold theory for dynamical systems (37D10) Inertial manifolds (35B42) Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems (37L25)
Related Items
A conservative Allen-Cahn equation with a space-time dependent Lagrange multiplier ⋮ The sharp interface limit for the stochastic Cahn-Hilliard equation ⋮ Stochastic Cahn-Hilliard equation in higher space dimensions: the motion of bubbles ⋮ Mass-conserving stochastic partial differential equations and backward doubly stochastic differential equations ⋮ Invariant manifolds of interior multi-spike states for the Cahn-Hilliard equation in higher space dimensions ⋮ Metastable dynamics for a hyperbolic variant of the mass conserving Allen-Cahn equation in one space dimension ⋮ Slow motion for the nonlocal Allen-Cahn equation in \(n\) dimensions ⋮ Motion of a Droplet for the Stochastic Mass-Conserving Allen--Cahn Equation ⋮ Fast explicit operator splitting method and time-step adaptivity for fractional non-local Allen-Cahn model ⋮ Numerical approximation of the conservative Allen–Cahn equation by operator splitting method ⋮ Time-fractional Cahn-Hilliard equation: well-posedness, degeneracy, and numerical solutions
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Spectral comparison principles for the Cahn-Hilliard and phase-field equations, and time scales for coarsening
- Approximately invariant manifolds and global dynamics of spike states
- Structured phase transitions on a finite interval
- The effect of a singular perturbation on nonconvex variational problems
- Geometric theory of semilinear parabolic equations
- Slow motion for the Cahn-Hilliard equation in one space dimension
- Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics
- Metastable patterns for the Cahn-Hilliard equation. I
- Metastable patterns for the Cahn-Hilliard equation. II: Layer dynamics and slow invariant manifold
- Slow dynamics for the Cahn-Hilliard equation in higher space dimensions: The motion of bubbles
- Motion of a droplet by surface tension along the boundary
- Convergence of the Cahn-Hilliard equation to the Hele-Shaw model
- The gradient theory of phase transitions and the minimal interface criterion
- Slow-motion manifolds, dormant instability, and singular perturbations
- Critical spectrum and stability of interfaces for a class of reaction-diffusion equations
- Equilibria with many nuclei for the Cahn-Hilliard equation
- Multiple spike layers in the shadow Gierer-Meinhardt system: Existence of equilibria and the quasi-invariant manifold
- The Dynamics of Nucleation for the Cahn–Hilliard Equation
- The Dynamics of a Conserved Phase Field System: Stefan-like, Hele-Shaw, and Cahn-Hilliard Models as Asymptotic Limits
- Invariant manifolds for metastable patterns in ut = ε2uxx—f(u)
- On the slowness of phase boundary motion in one space dimension
- On the slow dynamics for the Cahn–Hilliard equation in one space dimension
- Existence and persistence of invariant manifolds for semiflows in Banach space
- Slow dynamics for the cahn-hilliard equation in higher space dimension part i: spectral estimates∗
- Metastable patterns in solutions of ut = ϵ2uxx − f(u)
- Exixtance of equilibria for the chn-hilliard equation via local minimizers of the perimeter
- Free Energy of a Nonuniform System. I. Interfacial Free Energy
- Mullins-Sekerka motion of small droplets on a fixed boundary
