scholarly journals Fractional Diffusion Limit of a Kinetic Equation with Diffusive Boundary Conditions in the Upper-Half Space

2019 ◽  
Vol 235 (2) ◽  
pp. 1245-1288
Author(s):  
L. Cesbron ◽  
A. Mellet ◽  
M. Puel
Keyword(s):  
Kinetic Equation ◽  
Boundary Conditions ◽  
Half Space ◽  
Fractional Diffusion ◽  
Diffusion Limit ◽  
Diffusive Boundary

scholarly journals The time fractional diffusion equation and the advection-dispersion equation

2005 ◽  
Vol 46 (3) ◽  
pp. 317-330 ◽  
Author(s):  
F. Huang ◽  
F. Liu
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
Dispersion Equation ◽  
Half Space ◽  
Fractional Diffusion ◽  
Explicit Representation ◽  
Green Functions ◽  
Advection Dispersion ◽  
Whole Space ◽  
Time Fractional Diffusion Equation

AbstractThe time fractional diffusion equation with appropriate initial and boundary conditions in an n-dimensional whole-space and half-space is considered. Its solution has been obtained in terms of Green functions by Schneider and Wyss. For the problem in whole-space, an explicit representation of the Green functions can also be obtained. However, an explicit representation of the Green functions for the problem in half-space is difficult to determine, except in the special cases α = 1 with arbitrary n, or n = 1 with arbitrary α. In this paper, we solve these problems. By investigating the explicit relationship between the Green functions of the problem with initial conditions in whole-space and that of the same problem with initial and boundary conditions in half-space, an explicit expression for the Green functions corresponding to the latter can be derived in terms of Fox functions. We also extend some results of Liu, Anh, Turner and Zhuang concerning the advection-dispersion equation and obtain its solution in half-space and in a bounded space domain.

scholarly journals Fractional diffusion limit for a kinetic equation with an interface

2020 ◽  
Vol 48 (5) ◽  
pp. 2290-2322
Author(s):  
Tomasz Komorowski ◽  
Stefano Olla ◽  
Lenya Ryzhik
Keyword(s):  
Kinetic Equation ◽  
Fractional Diffusion ◽  
Diffusion Limit

scholarly journals Fractional diffusion limit of a linear kinetic equation in a bounded domain

2017 ◽  
Vol 10 (3) ◽  
pp. 541-551 ◽  
Author(s):  
Pedro Aceves-Sánchez ◽  
◽  
Christian Schmeiser
Keyword(s):  
Kinetic Equation ◽  
Bounded Domain ◽  
Fractional Diffusion ◽  
Diffusion Limit ◽  
Linear Kinetic

scholarly journals Generalized fractional Poisson process and related stochastic dynamics

2020 ◽  
Vol 23 (3) ◽  
pp. 656-693 ◽  
Author(s):  
Thomas M. Michelitsch ◽  
Alejandro P. Riascos
Keyword(s):  
Poisson Process ◽  
Continuous Time ◽  
Counting Process ◽  
Stochastic Dynamics ◽  
Waiting Times ◽  
Fractional Diffusion ◽  
Diffusion Limit ◽  
Fractional Operators ◽  
Fractional Poisson Process ◽  
Erlang Process

AbstractWe survey the ‘generalized fractional Poisson process’ (GFPP). The GFPP is a renewal process generalizing Laskin’s fractional Poisson counting process and was first introduced by Cahoy and Polito. The GFPP contains two index parameters with admissible ranges 0 < β ≤ 1, α > 0 and a parameter characterizing the time scale. The GFPP involves Prabhakar generalized Mittag-Leffler functions and contains for special choices of the parameters the Laskin fractional Poisson process, the Erlang process and the standard Poisson process. We demonstrate this by means of explicit formulas. We develop the Montroll-Weiss continuous-time random walk (CTRW) for the GFPP on undirected networks which has Prabhakar distributed waiting times between the jumps of the walker. For this walk, we derive a generalized fractional Kolmogorov-Feller equation which involves Prabhakar generalized fractional operators governing the stochastic motions on the network. We analyze in d dimensions the ‘well-scaled’ diffusion limit and obtain a fractional diffusion equation which is of the same type as for a walk with Mittag-Leffler distributed waiting times. The GFPP has the potential to capture various aspects in the dynamics of certain complex systems.

Smoluchowski problem for metals with mirror-diffusive boundary conditions

2009 ◽  
Vol 161 (1) ◽  
pp. 1403-1414 ◽  
Author(s):  
A. V. Latyshev ◽  
A. A. Yushkanov
Keyword(s):  
Boundary Conditions ◽  
Diffusive Boundary

Solution of Navier’s Equation in Cylindrical Curvilinear Coordinates

1978 ◽  
Vol 45 (4) ◽  
pp. 812-816 ◽  
Author(s):  
B. S. Berger ◽  
B. Alabi
Keyword(s):  
Fourier Transform ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Half Space ◽  
Coordinate Transformation ◽  
Numerical Results ◽  
Three Dimensions ◽  
Curvilinear Coordinates ◽  
Rectangular Region

A solution has been derived for the Navier equations in orthogonal cylindrical curvilinear coordinates in which the axial variable, X3, is suppressed through a Fourier transform. The necessary coordinate transformation may be found either analytically or numerically for given geometries. The finite-difference forms of the mapped Navier equations and boundary conditions are solved in a rectangular region in the curvilinear coordinaties. Numerical results are given for the half space with various surface shapes and boundary conditions in two and three dimensions.

Exact solutions of multi-term fractional diffusion-wave equations with Robin type boundary conditions

2013 ◽  
Vol 35 (1) ◽  
pp. 49-62 ◽  
Author(s):  
Xiao-jing Liu ◽  
Ji-zeng Wang ◽  
Xiao-min Wang ◽  
You-he Zhou
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Wave Equations ◽  
Fractional Diffusion ◽  
Diffusion Wave ◽  
Type Boundary
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