Dynamic diffusion-type equations on discrete-space domains

Space–time fractional diffusion on bounded domains

Pullback D-attractors for non-autonomous partly dissipative reaction-diffusion equations in unbounded domains

At present paper, we establish the existence of pullback $mathcal{D}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $L^2(mathbb{R}^n)times L^2(mathbb{R}^n)$. In order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{D}$-absorbing set, is pullback $widehat{D}_0$-asymptotically compact.

Classical , Nonlocal , and Fractional Diffusion Equations on Bounded Domains

The purpose of this paper is to compare the solutions of one-dimensional boundary value problems corresponding to classical, fractional and nonlocal diffusion on bounded domains. The latter two diffusions are viable alternatives for anomalous diffusion, when Fick’s first law is an inaccurate model. In the case of nonlocal diffusion, a generalization of Fick’s first law in terms of a nonlocal fl...

Fundamental Domains of Discrete Groups Acting on Euclidean Space

Fundamenatal domains of wallpaper groups acting on R2 whose closures are homeomorphic to closed disks can be classified in the same way that Grunbaum classifies isohedral plane tilings in [7]. Almost all of these types of fundamental domains appear as Dirichlet domains, and examples are given.

Discrete-space partial dynamic equations on time scales and applications to stochastic processes

We consider a general class of discrete-space linear partial dynamic equations. The basic properties of solutions are provided (existence and uniqueness, sign preservation, maximum principle). Above all, we derive the following main results: first, we prove that the solutions depend continuously on the choice of the time scale. Second, we show that, under certain conditions, the solutions descr...