| 分数阶非线性对流-扩散方程及其解 |
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| 引用本文： | 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].山东大学学报(理学版),2007,42(1):35-39. |
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| 作者姓名： | 刘艳芹 徐明瑜 蒋晓芸 |
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| 作者单位： | 1. 德州学院,数学系,山东,德州,253023;山东大学,数学与系统科学学院,山东,济南,250100
2. 山东大学,数学与系统科学学院,山东,济南,250100 |
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| 基金项目： | 国家自然科学基金;高等学校博士学科点专项科研项目 |
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| 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.
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| 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 |
| 文章编号： | 1671-9352（2007）01-0035-05 |
| 收稿时间： | 2006-04-25 |
| 修稿时间： | 2006-04-25 |
The fractional nonlinear convection-diffusion equation and its solution |
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| LIU Yan-qin,XU Ming-yu,JIANG Xiao-yun.The fractional nonlinear convection-diffusion equation and its solution[J].Journal of Shandong University,2007,42(1):35-39. |
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| Authors: | LIU Yan-qin XU Ming-yu JIANG Xiao-yun |
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| Institution: | 1. Department of Mathematics, Dezhou Univ., Dezhou 253023, Shandong, China; 2. School of Math. and System Sci., Shandong Univ. , Jinan 250100, Shandong, China |
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| Abstract: | Fractional nonlinear convection diffusion equation with external forces is given. First, the integer equation is studied by considering the diffusion coefficient D(x)∝xθ. 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. |
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| Keywords: | nonlinear equation fractional calculus q-exponential function q-logarithm function Tsallis entropy |
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