In this paper, we discuss the steady state Fractional Advection Dispersion Equation (FADE) on bounded domains in IRd . Fractional differential and integral operators are defined and analyzed. Appropriate fractional derivative spaces are defined, and shown to be equivalent to the fractional dimensional Sobolev spaces. A theoretical framework for the variational solution of the steady state FADE ...

We consider the initial value problem for generalized Fornberg-Whitham equation, which consists of p-order nonlinear advection term and nonlocal dispersion term. In case p=2, we study sufficient conditions blow-up solutions some relations to Burgers equation. Also, p?5, show global existence with small data.

An analytical study is presented of dispersion in steady and oscillatory open-channel flows under the combined effects due to reversible sorptive phase exchange with the bed and irreversible air–water reaction on the free surface. The free-surface reaction is assumed to be so weak that the asymptotic mean concentration can be developed well before undue substantial loss to the air occurs. The e...

The numerical simulation of aeroacoustic phenomena requires high-order accurate numerical schemes with low dispersion and low dissipation errors. A technique has recently been devised in a Computational Fluid Dynamics framework which enables optimal parameters to be chosen so as to better control the grade and balance of dispersion and dissipation in numerical schemes Appadu and Dauhoo, 2011; A...

In this paper some analytical solutions of the advection-dispersion equation are proposed and adopted to solve a non-linear parameter estimation problem. To test the robustness of the analytical solutions if adopted in inverse problems, the anisotropic dispersion coefficients are estimated using sets of experimental data simulated by Monte Carlo techniques. Cylindrical geometry is considered si...

Analytical solutions are obtained for one-dimensional advection-diffusion equation with variable coefficients in longitudinal semi-infinite homogeneous porous medium for uniform flow. The solute dispersion parameter is considered temporally dependent while the velocity of the flow is considered uniform. The first order decay and zero-order production terms are considered inversely proportional ...

Many microorganisms live within surface-associated consortia, termed biofilms, that can form intricate porous structures interspersed with a network of fluid channels. In such systems, transport phenomena, including flow and advection, regulate various aspects of cell behavior by controlling nutrient supply, evacuation of waste products, and permeation of antimicrobial agents. This study presen...