对称方法在非线性偏微分方程边值问题中的应用  

Application of the Symmetry Method on Boundary Value Problems of Nonlinear Partial Differential Equations

作　　者：王晓民[1] 苏道毕力格[1] 特木尔朝鲁[2] 

机构地区：[1]内蒙古工业大学理学院,呼和浩特010051 [2]上海海事大学文理学院,上海200135

出　　处：《内蒙古大学学报（自然科学版）》2013年第2期129-132,共4页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金资助项目(No.11071159);内蒙古高等学校科学技术研究资助项目(NJZY12056);内蒙古自然科学基金资助项目(No.2010MS0115);内蒙古工业大学科学研究资助项目(No.ZS201033)

摘　　要：研究了微分方程对称方法在非线性偏微分方程边值问题中的应用,即利用给定偏微分方程的多参数对称,将偏微分方程边值问题约化为常微分方程初值问题.作为应用,利用对称方法解决了力学中的两个非线性偏微分方程组边值问题,包括流体力学中的非线性边值问题和自然对流方程的边值问题.确定微分方程对称时吴-微分特征列集算法起到了关键性作用.Application of the symmetry method on boundary value problems of nonlinear partial differ-ential equations is studied. By using the multi-parameter symmetry of a given partial differential equation, the boundary value problem of the partial differential equation can be reduced to an initial value problem of the original differential equation. As applications, two nonlinear boundary value problems in mechanics are solved by using the symmetry method, including the nonlinear boundary value problems in fluid mechanics and the boundary value problems of free convection equations. In determining the symmetry of a differential equation, Wu-differential characteristic set algorithm plays an important role.

关 键 词：偏微分方程边值问题 对称方法 吴-微分特征列集算法 

分 类 号：O175.29[理学—数学]