In this paper, we propose a model for multi-color image inpainting composed of n colors. In particular, as in the binary model, i.e., the Bertozziâ€“Esedogluâ€“Gilletteâ€“Cahnâ€“Hilliard equation (Bertozziâ€¦ (More)

This paper is concerned with the nonisentropic unipolar hydrodynamic model of semiconductors in the form of multi-dimensional full EulerPoisson system. By heuristically analyzing the exact gapsâ€¦ (More)

Our aim in this article is to construct exponential attractors for singularly perturbed damped wave equations that are continuous with respect to the perturbation parameter. The main difficulty comesâ€¦ (More)

The utilization of incremental unknowns was proposed in [21] as a tool for the approximation of inertial manifolds ([6], [7]) when finite differences discretizations are used. In a first step theâ€¦ (More)

We consider in this article the damped and driven two-dimensional Navierâ€“Stokes equations at the limit of small viscosity coefficient Î½â†’0. In particular, we obtain upper bounds of the order Î½ on theâ€¦ (More)

In this article, we construct robust (i.e. lower and upper semicontinuous) exponential attractors for singularly perturbed phase-field type equations. Moreover, we obtain estimates for the symmetricâ€¦ (More)

In this article, we study the long time behavior of a phase-field parabolichyperbolic system arising from the phase-field theory of phase transitions. This system consists of a parabolic equationâ€¦ (More)

Our aim in this note is to study the existence and uniqueness of solutions to a phase-field system, based on type III heat conduction, with a logarithmic potential. The main difficulty is to proveâ€¦ (More)

The Cahn-Hilliard equation is very important in materials science. It is a conservation law which describes important qualitative behaviors of two-phase systems, namely, the phase separation processâ€¦ (More)