分数阶非线性对流-扩散方程及其解

分数阶非线性对流-扩散方程及其解

刘艳芹¹^,²，徐明瑜²，蒋晓芸²

1.德州学院数学系, 山东德州253023; 2.山东大学数学与系统科学学院, 山东济南250100

收稿日期:2006-04-25 修回日期:1900-01-01 出版日期:2006-10-24 发布日期:2006-10-24
通讯作者: 刘艳芹¹^,²

The fractional nonlinear convection-diffusion equation and its solution

LIU Yan-qin¹^,²,XU Ming-yu² and JIANG Xiao-yun²

1. Department of Mathematics, Dezhou Univ., Dezhou 253023, Shandong, China; 2. School of Math. and System Sci., Shandong Univ., Jinan 250100, Shandong, China

Received:2006-04-25 Revised:1900-01-01 Online:2006-10-24 Published:2006-10-24
Contact: LIU Yan-qin¹,²

摘要/Abstract

摘要： 建立了含有外力的分数阶非线性对流-扩散方程.讨论了具有扩散系数D(x)∝x^-^θ的整数阶方程,利用q-指数函数和q-对数函数的特性,求得了解析解.考虑吸附效应的分数阶方程,在非线性参量满足某种关系的情况下,求得了精确特解,并研究了解的渐近行为.

关键词: 非线性方程, 分数阶微积分, Tsallis 熵 , q-对数函数, q-指数函数

Abstract: Fractional nonlinear convectiondiffusion equation with external forces is given. First, the integer equation is studied by considering the diffusion coefficient D(x)∝x^θ. By using the q-exponential function and q-logarithm function, the analytical solution of the equation is derived. Second, a fractional equation with absorption is analyzed. On condition that the nonlinear parameters satisfy certain relationships, a special solution can be obtained. In addition, the asymptotic behaviors for the solution are also discussed.

Key words: Tsallis entropy , q-logarithm function, q-exponential function, fractional calculus, nonlinear equation

中图分类号:

O175.29

刘艳芹,徐明瑜,蒋晓芸 . 分数阶非线性对流-扩散方程及其解[J]. J4, 2007, 42(1): 35-39 .

LIU Yan-qin,XU Ming-yu and JIANG Xiao-yun . The fractional nonlinear convection-diffusion equation and its solution[J]. J4, 2007, 42(1): 35-39 .

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