分数阶非线性对流-扩散方程及其解  

The fractional nonlinear convection-diffusion equation and its solution

作　　者：刘艳芹[1] 徐明瑜[2] 蒋晓芸[2] 

机构地区：[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

出　　处：《山东大学学报（理学版）》2007年第1期35-39,63,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(10272067);教育部博士点专项科研基金资助项目(20030422046)

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.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 pa- rameters satisfy certain relationships, a special solution can be obtained. In addition, the asymptotic behaviors for the solution are also discussed.

关 键 词：非线性方程 分数阶微积分 q-指数函数 q-对数函数 TSALLIS 熵 

分 类 号：O175.29[理学—数学] O175.23[理学—基础数学]