Transient anomalous sub-diffusion on bounded domains

Transient Anomalous Sub-diffusion on Bounded Domains.

This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractional derivatives is solved. Then a separation of variables and eigenfunction expansions in time and space are used to write strong solutions. Finally, stochastic solutions are written in terms of an inverse subordinator.

Space–time fractional diffusion on bounded domains

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...

Multiscale Homogenization with Bounded Ratios and Anomalous Slow Diffusion

Abstract We show that the effective diffusivity matrix D(V n) for the heat operator ∂t − (1/2 − ∇V n∇) in a periodic potential V n = n k=0 Uk(x/Rk) obtained as a superposition of Hölder-continuous periodic potentials Uk (of period Td := R d/Zd , d ∈ N∗, Uk(0) = 0) decays exponentially fast with the number of scales when the scale ratios Rk+1/Rk are bounded above and below. From this we deduce t...

Shearlets on Bounded Domains

Shearlet systems have so far been only considered as a means to analyze L2-functions defined on R2, which exhibit curvilinear singularities. However, in applications such as image processing or numerical solvers of partial differential equations the function to be analyzed or efficiently encoded is typically defined on a non-rectangular shaped bounded domain. Motivated by these applications, in...