We prove well-posedness and regularity of solutions to a fractional diffusion porous media equation with variable order that may depend on the unknown solution. present linearly implicit time-stepping method linearize discretize in time, rigorous analysis for convergence numerical based proved results.

This paper concerns two-dimensional incompressible magnetohydrodynamic (MHD) equations with damping only in the vertical component of velocity and horizontal diffusion magnetic equations. If field is not taken into consideration system reduced to Euler-like an extra Riesz transform-type term. The global well-posedness remains open problem whole plane R2. When coupled field, stability for MHD R2...

Plants with hypoglycemic properties are important in the treatment of diabetes. One of the mechanisms in reducing blood glucose is preventing the digestive absorption of glucose. The aim of this study was to evaluate the antioxidant properties of some traditional medicinal plants collected from different regions of Iran and their effects on glucose diffusion decrease. The amounts of phenolic co...

A one parameter family of equations is considered which connects the well-known Perona-Malik equation to standard diffusion. The parameter acts as a regularization parameter which gradually modifies the ill-posed Perona-Malik equation, through a strongly locally well-posed equation, to a strongly globally well-posed one which exhibits a behavior akin to that of standard diffusion, which is itse...

Forward-and-backward (FAB) diffusion is a method for sharpening blurry images (Gilboa et al. 2002). It combines forward diffusion with a positive diffusivity and backward diffusion where negative diffusivities are used. The well-posedness properties of FAB diffusion are unknown, and it has been observed that standard discretisations can violate a maximum-minimum principle. We show that for a no...

Nanowire superlattices (NWSLs) are objects with a wide range of potential applications in nanoscale electronics and photonics. These objects are already grown experimentally in laboratories and studies of their properties represent an important task in nanotechnology research. Tools of mathematical modelling provide a powerful means for studying these fascinating structures with an ultimate goa...

As adolescent Internet use grew exponentially in the last decade, with it emerged a number of correspondent expectations. Among them were the following: (1) that gender predicts usage, i.e., that boys spend more time online, surfing the web and playing violent games, while girls chat or shop online; (2) that Internet use causes social isolation and depression, especially for teens; and (3) that...

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