论二个自变量常系数线性偏微分方程i+j≤n aijpiqjφ=0的解的构造
On the Structure of Solutions of Linear Partial Differential Equation i+j≤n aijpiqjφ=0 With Two Independent Variables and Constant Coefficients
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摘要: 本文是文[1]的继续.对更广泛的一类二个自变量常系数线性偏微分方程的求解方法作了详细地研究,给出了解的一般表示,这种表示可用来逼近具体问题的定解条件.为说明所得结果的运用.文中举出了具体的力学应用实例.Abstract: This paper is a continuation of [1]. In this paper, the solutions of the more general linear partial differential equation form with two independent variables and constant coefficients are discussed in detail. The general solution which can be used in the approximation to the conditions of the definite solution of the practical problems is presented. To illustrate the use of the results obtained in this paper, some practical examples in mechanics are given.
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[1] 盖秉政,椭圆型方程的解及其在力学上的应用,应用数学和力学,2,4(1981),445. [2] Михлин С.Г.,Плоская деформация в анизотропной среде,Трубы Сейсмолошч,Инта АН СССР,76(1936)76(1936). [3] Timoshenko,S,P,Theory of Plates and Shells,McGraw-Hill,New York(1940). [4] Лурье А.И.,Коннентрапия напряжений в области отверстия на поверхности кругового цилиндра ПММ,103(1946),397. -
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