Attractors for dissipative partial differential equations in bounded and unbounded domains

A Miranville, S Zelik - Handbook of differential equations: evolutionary …, 2008 - Elsevier
Publisher Summary The study of the asymptotic behavior of dynamical systems arising from
mechanics and physics is a capital issue because it is essential for practical applications to …

Recent developments in dynamical systems: three perspectives

F Balibrea, T Caraballo, PE Kloeden… - International Journal of …, 2010 - World Scientific
RECENT DEVELOPMENTS IN DYNAMICAL SYSTEMS: THREE PERSPECTIVES | International
Journal of Bifurcation and Chaos World Scientific Search This Journal Anywhere Quick …

A robust and efficient fingerprint image restoration method based on a phase-field model

Y Li, Q Xia, C Lee, S Kim, J Kim - Pattern Recognition, 2022 - Elsevier
In this study, we present a robust and efficient fingerprint image restoration algorithm using
the nonlocal Cahn–Hilliard (CH) equation, which was proposed for modeling the …

On the 2D Cahn–Hilliard equation with inertial term

M Grasselli, G Schimperna, S Zelik - Communications in Partial …, 2009 - Taylor & Francis
Galenko et al. proposed a modified Cahn–Hilliard equation to model rapid spinodal
decomposition in non-equilibrium phase separation processes. This equation contains an …

Kinetic contribution to the fast spinodal decomposition controlled by diffusion

P Galenko, D Jou - Physica A: Statistical Mechanics and its Applications, 2009 - Elsevier
Analysis of a model for fast spinodal decomposition controlled by diffusion is proposed.
Using the concept of fast phase separation, an interpretation of a purely non-equilibrium …

On the 3D Cahn–Hilliard equation with inertial term

M Grasselli, G Schimperna, A Segatti… - Journal of Evolution …, 2009 - Springer
We study the modified Cahn–Hilliard equation proposed by Galenko et al. in order to
account for rapid spinodal decomposition in certain glasses. This equation contains, as …

Asymptotic behavior of a nonisothermal viscous Cahn–Hilliard equation with inertial term

M Grasselli, H Petzeltová, G Schimperna - Journal of Differential Equations, 2007 - Elsevier
We consider a differential model describing nonisothermal fast phase separation processes
taking place in a three-dimensional bounded domain. This model consists of a viscous Cahn …

Trajectory and smooth attractors for Cahn–Hilliard equations with inertial term

M Grasselli, G Schimperna, S Zelik - Nonlinearity, 2010 - iopscience.iop.org
This paper is devoted to a modification of the classical Cahn–Hilliard equation proposed by
some physicists. This modification is obtained by adding the second time derivative of the …

Coarse graining for the phase-field model of fast phase transitions

D Jou, PK Galenko - Physical Review E—Statistical, Nonlinear, and Soft …, 2013 - APS
Fast phase transitions under lack of local thermalization between successive elementary
steps of the physical process are treated analytically. Non-Markovian master equations are …

Invariant sample measures and sample statistical solutions for nonautonomous stochastic lattice Cahn-Hilliard equation with nonlinear noise

J Wang, D Zhu, C Li - arXiv preprint arXiv:2404.14798, 2024 - arxiv.org
We consider a stochastic lattice Cahn-Hilliard equation with nonautonomous nonlinear
noise. First, we prove the existence of pullback random attractors in $\ell^ 2$ for the …