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Functional Separable Solutions to Nonlinear Diffusion Equations by Group Foliation Method

ISSN号：0253-6102
期刊名称：《理论物理通讯：英文版》
时间：0
分类：O175.29[理学—数学;理学—基础数学]
作者机构：[1]Center for Nonlinear Studies, Northwest University, Xi＇an 710069, China, [2]Department of Mathematics, Northwest University, Xi＇an 710069, China, [3]Department of Mathematics, South-Central University of Nationalities, Wuhan 430074, China, [4]Wuhan Institute of Physics and Mathematics, the Chinese Academy of Sciences, Wuhan 430071, China
相关基金：The project supported by National Natural Science Foundation of China under Grant No. 10371098 and the Program for New Century Excellent Talents in Universities under Grant No. NCET-04-0968

作者： HU Jia-Yi[1,2,3], QU Chang-Zheng[1,2], YIN Hui[4]

关键词：非线性扩散方程, 函数分离解, 对称群, 群叶状结构法, group foliation method, functional separation of variable, nonlinear diffusion equation, symmetry group

中文摘要：

我们与来源和传送对流术语一起考虑变量的功能的分离到非线性的散开方程：u_t =((x) D (u) u_x )_x + B (x) Q (u) ， A_x ≠ 0。到这个方程的变量的 Thefunctional 分离被使用组生叶 method.A 分类学习为承认函数的方程被执行可分离的解决方案。作为后果，产生方程的一些答案被获得。

英文摘要：

We consider the functional separation of variables to the nonlinear diffusion equation with source and convection term： ut = （A（x）D（u）ux）x ＋ B（x）Q（u）, Ax ≠ 0. The functional separation of variables to this equation is studied by using the group foliation method. A classification is carried out for the equations which admit the function separable solutions. As a consequence, some solutions to the resulting equations are obtained.

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