一类复合型二阶线性偏微分方程边值问题解的相似构造法  

A Similar Construction Method for Solving Boundary Value Problems of a Composite Second-Order Homogeneous Linear Partial Differential Equation

作　　者：钱雪 郑鹏社 

机构地区：[1]西华大学理学院,四川 成都

出　　处：《理论数学》2024年第5期9-17,共9页Pure Mathematics

摘　　要：本文研究了一类复合型二阶线性偏微分方程边值问题,通过将此类复合型偏微分方程的解式进行整理和化简,发现其解式是由左区和右区的引解函数、衔接性条件以及内外区条件的系数组装成的,而引解函数是由微分方程的两个线性无关解构成,且其解具有相似结构的形式,于是提出了求解此类复合型偏微分方程边值问题的相似构造法。经研究发现:相似构造法不仅能够使得部分边值问题的解答过程更加精简、降低了求解此类方程的难度且解式优美,还进一步揭示了解的内在性质和规律,为解决相应的数学问题以及油气藏等方面的工程问题提供了相适合的工具,也为部分软件分析的理论知识打下了基础。In this paper, we study the boundary value problem of a class of composite second-order linear partial differential equations, and by sorting out and simplifying the solutions of such composite partial differential equations, it is found that the solution is composed of the induction function of the left and right regions, the cohesive condition and the coefficient of the inner and outer region conditions, and the induction function is composed of two linear independent solutions of the differential equation, and the solutions have a similar structure. It is found that the similarity construction method can not only simplify the solution process of some boundary value problems, reduce the difficulty of solving such equations and solve them beautifully, but also further reveal the intrinsic properties and laws of understanding, provide suitable tools for solving corresponding mathematical problems and engineering problems in oil and gas reservoirs, and also lay a foundation for the theoretical knowledge of some software analysis.

关 键 词：相似核函数 边值问题 复合微分方程 相似构造 

分 类 号：O17[理学—数学]