Invariant Sets and Exact Solutions to Nonlinear Diffusion Equations with x-Dependent Convection and Absorption  

作　　者：JIA Hua-Bing XU Wei 

机构地区：[1]Department of Applied Mathematics, Northwestern Polytechnical University, Xi＇an 710072, China [2]Department of Matheinatics, Baoji University of Arts and Sciences, Baoji 721013, China

出　　处：《Communications in Theoretical Physics》2008年第10期821-826,共6页理论物理通讯（英文版）

基　　金：National Natural Science Foundation of China under Grant Nos.10472091,10332030,and 10502042;the Natural Science Foundation of Shaanxi Province under Grant No.2003A03

摘　　要：In this paper, we introduce a new invariant set Eo={u：ux=f＇（x）F（u）＋ε[g＇（x）-f＇（x）g（x）]F（u）×exp（-∫^u1/F（z）dz）}where f and g are some smooth functions of x, ε is a constant, and F is a smooth function to be determined. The invariant sets and exact sohltions to nonlinear diffusion equation ut = （ D（u）ux）x ＋ Q（x, u）ux ＋ P（x, u）, are discussed. It is shown that there exist several classes of solutions to the equation that belong to the invariant set Eo.

关 键 词：invariant set exact solution nonlinear diffusion equations rotation group scaling group 

分 类 号：O175[理学—数学]