Analytic Solutions of a Class of Nonlinear Partial Differential Equations
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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．Abstract: Firstly, an approach is presented for computing the adjoint 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 mathe-matics-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.
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Key words:
- AC=BD model /
- partial- nonlinear /
- adjoint /
- conjugate /
- plate and shell
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