瞬时点源分数阶超常扩散的浓度分布

段俊生; 徐明瑜

瞬时点源分数阶超常扩散的浓度分布

段俊生¹,
徐明瑜²

1.
天津商学院, 基础部, 天津, 300134;
2.
山东大学, 数学与系统科学学院, 济南, 250100

基金项目: 国家自然科学基金资助项目(10272067);教育部博士点基金资助项目(1999042211)

详细信息

作者简介:
段俊生(1965- ),男,呼和浩特人,副教授,博士(E-mil:duanjssdu@sina.com).

中图分类号: O175.6
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- 被引次数: 0
出版历程
- 收稿日期: 2001-07-04
- 修回日期: 2003-07-02
- 刊出日期: 2003-11-15

The Concentration Distribution of Fractional Anomalous Diffusion Caused by an Instantaneous Point Source

DUAN Jun-sheng¹,
XU Ming-yu²

1.
Department of Basic Sciences, Tianjin University of Commerce, Tianjin 300134, P. R. China;
2.
Institute of Mathematics and Systematical Science, Shandong University, Jinan 250100, P. R. China

摘要

摘要: 利用质量守恒条件、解的时空相似性、Mellin变换以及Fox函数理论,给出n维空间中(n=1,2,3)瞬时点源分数阶超常扩散浓度分布的Fox函数表示及解析表达式,并讨论其渐近性质.
- 瞬时点源 /
- 超常扩散 /
- 分数阶微积分 /
- Fox函数 /
- Mellin变换
Abstract: The Fox function expression and the analytic expression for the concentration distribution of fractional anomalous diffusion caused by an instantaneous point source in n-dimensional space(n=1, 2 or 3) are derived by means of the condition of mass conservation, the time-space similarity of the solution, Mellin transform and the properties of the Fox function. And the asymptotic behaviors for the solutions are also given.
- instantaneous point source /
- anomalous diffusion /
- fractional calculus /
- Fox function /
- Mellin transform

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参考文献(12)

[1]	Giorna M,Roman H E.Fractional diffusion equation for transport phenomena in random media[J].Physica A,1992,185(1):87-97.
[2]	REN Fu-yao,LIANG Jin-rong,WANG Xiao-tian.The determination of the diffusion kernel on fractals and fractional diffusion equation for transport phenomena in random media[J].Physics Letters A,1999,252(3):141-150.
[3]	West B J,Grigolini P,Metzler R,et al.Fractional diffusion and Levy stable processes[J].Physical Review E,1997,55(1):99-106.
[4]	Nigmatullin R R.The realization of the generalized transfer equation in a medium with fractal geometry[J].Phys Status Solidi B,1986,133(1):425-430.
[5]	ZENG Qiu-hua,LI Hou-qiang.Diffusion equation for disordered fractal media[J].Fractals,2000,8(1):117-121.
[6]	Wyss W.The fractional diffusion equation[J].JMathPhys,1986,27(11):2782-2785.
[7]	Mainardi F.Fractional relaxation-oscillation and fractional diffusion-wave phenomena[J].Chaos,Solitons and Fractals,1996,7(9):1461-1477.
[8]	Schneider W R,Wyss W.Fractional diffusion and wave equations[J].J Math Phys,1989,30(1):134-144.
[9]	Gorenflo R,Luchko Y,Mainardi F.Wright functions as scale-invariant solutions of the diffusion-wave equation[J].J Comp Appl Math,2000,118(1):175-191.
[10]	Malnardi F,Gorenfio R.On Mittag-Leffler-type function in fractional evolution processes[J].J Comp Appl Math,2000,118(2):283-299.
[11]	Glockle W G,Nonnenmacher T F.Fox fiunction representation of non-debye relaxation processes[J].J Stat Phys,1993,71(3/4):741-757.
[12]	Mathal A M,Saxena R K.The H-Function with Applications in Statistics and Other Disciplines[M].New Delhi:Wiley Eastern Limited,1978.