CAJ | 학술논문

对含任意参数(函数)的微分方程进行对称群分类是经典 Lie 对称理论在微分方程中的主要应用之一，而获得分类方程、求解确定方程组是进行有效对称分类的关键。给出含两个任意函数的二维边界层系统的经典 Lie 对称分类，并构造了其不变解。
대함임의삼수(함수)적미분방정진행대칭군분류시경전 Lie 대칭이론재미분방정중적주요응용지일，이획득분류방정、구해학정방정조시진행유효대칭분류적관건。급출함량개임의함수적이유변계층계통적경전 Lie 대칭분류，병구조료기불변해。
Symmetry classfication of partial differential equations with arbitrary parameters (or functions)is one of the main applications of classical Lie theory to differential equations.The key point to determine the symmetry classification is to find out classification equations and solve determining equa-tions.In this paper,symmetry classification and some corresponding invariant solutions of two-dimensional boundary layer system with arbitrary functions f (u)and g (v)are given.