非齐次线性算子方程组一般解的代数构造

证明非次线性算子方程组Ａｕ＝ｆ的一般解为ｕ＝Ｃｖ＋ｅ；其中ｖ满足方程组Ｄｖ＝ｇ，Ｄ是对角形矩阵，用代数方法给出Ｃ，Ｄ和ｅ的具体构造。用此方法可以给出各种弹性力学位函数和应力函数的机械化算法，构造数学物理中一系列方程的一般解。作为应用，给出线性各向同性热弹性理论方程组，各向同性微极弹性理论方程组和Ｍａｘｗｅｌｌ方程组的一般解。

Algebraic structure of general solutions to system of non-homogenous linear operator equations

It is proved that the general solutions to.the system of non-homogenous linear operator equation Au=f can be represented as u=Cv+e, where v satisfies Dv=g and D is a diagonal matrix. The constructions of C, D and e are given by the algebraic method. Using the method,authors can get a lot of mechanic algorithms of the elasticity displacement function and the stress function,and construct the general solutions to a series of etluations in mathematical physics As applications,authors have obtained the general solutions to the system of linear thermoelasticity for isoeropic elastic body equations, the system of micro-elasticity for isotropic elastic body and the Maxwell's equations.