一类非线性偏微分方程组的解析解  

Analytic Solutions of a Class of Nonlinear Partial Differential Equations

作　　者：张鸿庆[1] 丁琦[1] 

机构地区：[1]大连理工大学应用数学系,辽宁大连116024

出　　处：《应用数学和力学》2008年第11期1268-1278,共11页Applied Mathematics and Mechanics

基　　金：国家重点基础研究专项基金资助项目(2004CB318000)

摘　　要：首先,利用共轭算子的性质,将张鸿庆等提出的求伴随算子对的方法推广到了求一类非线性(即部分非线性的)算子矩阵的伴随算子向量.其次,利用机械化的构造方法给出了求解一类非线性(即,部分非线性的,且以所有线性的为其特例)非齐次微分方程组的统一理论,即通过齐次化和三角化求得恰当的变换,从而将原方程组化为较简单的形式,一般为对角化的.最后利用该方法求得了一些弹性力学方程组的解析解.Flrstly, an approach is presented for computing the aOjoint operator vector of a class of nonlinear （i. e. partial-nonlinear） operator matrix by generalizing the method presented by Zhang et al. and the conjugate operators. Secondly, a united theory is given for solving a class of nonlinear （i. e. partial-nonlinear and including all linear ） and non-homogeneous differential equations by the mathematics-mechanization method. In other words, a transformation is constructed by homogenization and triangulation which can reduce the original system to the simpler one which is diagonal, Finally, some practical applications are given in elasticity equations.

关 键 词：AC=BD模 部分非线性 伴随 共轭 板壳 

分 类 号：O175.2[理学—数学]