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扰动扩散方程初值问题的近似对称约化
引用本文:李吉娜,朱晓宁,程利芳.扰动扩散方程初值问题的近似对称约化[J].物理学报,2013,62(2):20201-020201.
作者姓名:李吉娜  朱晓宁  程利芳
作者单位:1. 中原工学院理学院,郑州,450007
2. 河南商业高等专科学校基础教学部,郑州,450044
基金项目:国家自然科学基金(批准号: 11101332)和河南省自然科学基金(批准号: 102300410275, 122300410166)资助的课题.
摘    要:本文利用近似广义条件对称方法研究一类带有源项的非线性扩散方程的初值问题.给出所研究方程的分类并将偏微分方程的初值问题约化为常微分方程的初值问题,通过求解约化后的常微分方程组可得相对应偏微分方程初值问题的近似解.

关 键 词:扰动扩散方程  初值问题  近似广义条件对称
收稿时间:2012-06-10

Approximate symmetry reduction for initial-value problem of perturbed diffusion equations
Li Ji-Na,Zhu Xiao-Ning,Cheng Li-Fang.Approximate symmetry reduction for initial-value problem of perturbed diffusion equations[J].Acta Physica Sinica,2013,62(2):20201-020201.
Authors:Li Ji-Na  Zhu Xiao-Ning  Cheng Li-Fang
Institution:1. College of Science, Zhong yuan University of Technology, Zhengzhou 450007, China;2. Department of General Studies, Henan Business College, Zhengzhou 450044, China
Abstract:In this paper, the approximate symmetry reduction for the initial-value problem of perturbed diffusion equations with source term is studied by the approximate generalized conditional symmetry. The classification of governing equations is given, and the Cauchy problem of partial differential equations is reduced to initial-value problem of ordinary differential equations. Finally, the approximate solution is obtained by solving the reduced system of equations.
Keywords:perturbed diffusion equation  initial-value problem  approximate generalized conditional symmetry
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