Our aim in this article is to review and discuss the Cahn–Hilliard equation, as well as someof its variants. Such variants have applications in, e.g., biology and image inpainting.
Our aim in this paper is to study the well-posedness and the dissipativity for a reformulation of the Caginalp phase-field system based on the Maxwell–Cattaneo law, instead of the usual Fourier law, ...for heat conduction. In particular, instead of the equation for the relative temperature (or the thermal displacement variable), we consider here the equation for the enthalpy.
Our aim in this paper is to study the asymptotic behavior, in terms of finite-dimensional attractors, of a sixth-order Cahn-Hilliard system. This system is based on a modification of the ...Ginzburg-Landau free energy proposed in Torabi S., Lowengrub J., Voigt A., Wise S., A new phase-field model for strongly anisotropic systems, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 2009, 465(2105), 1337–1359, assuming isotropy.
Our aim in this paper is to study a Cahn–Hilliard type system based on microconcentrations. We prove the existence and uniqueness of solutions to this system and then prove the convergence of the ...solutions to those of the original Cahn–Hilliard equation as a small parameter goes to zero, on finite time intervals.
Our aim in this article is to study generalizations of the conserved Caginalp phase-field system based on the Maxwell-Cattaneo law with two temperatures for heat conduction and with logarithmic ...nonlinear terms. We obtain well-posedness results and study the asymptotic behavior of the associated system. In particular, we prove the existence of the global attractor and prove the strict separation to the pure phases in two space dimensions. Furthermore, we give some numerical simulations, obtained with the FreeFem++ software
23
, comparing the conserved Caginalp phase-field type model with regular and with logarithmic nonlinear terms.
This paper is concerned with the Gromov–Hausdorff stability of global attractors for the 3D Navier–Stokes equations with damping under variations of the domain, which describes the complexity of the ...dynamics of the motion of a fluid flow. The Gromov–Hausdorff stability accounts for the Gromov–Hausdorff distance between two global attractors which may lie in disjoint phase spaces, as well as the stability of global attractors under perturbations of the domain. The same phase space cannot be used for the convergence via the Gromov–Hausdorff distance, which can be overcome, following Lee et al.(2020), by introducing a Banach space defined on a variable domain without “pull-backing” the perturbed system onto the original domain.
PDF
