三角形区域上复合边值问题探讨  

On triangular compound boundary problem

作　　者：胡洁[1] 刘华[1] 

机构地区：[1]天津职业技术师范大学理学院,天津300222

出　　处：《天津职业技术师范大学学报》2016年第4期40-44,共5页Journal of Tianjin University of Technology and Education

摘　　要：针对三角形区域上的复合边值问题,采用问题转化求解的办法,研究该问题的解析解。利用SchwarzChristoffel公式给出圆域到三角形区域的共形映射,依据椭圆函数的相关理论推导出三角形区域到圆域的逆映射;将三角形区域上的复合边值问题转化为圆域上的复合边值问题,进一步通过消去法把复合边值问题化为带间断系数的Hilbert边值问题,通过解析延拓化为带间断系数的联结问题,得出三角区域上复合边值问题的解析解。In view of the compound boundary value problem on the triangle region, the solution of the problem is solved by using the method of problem solving. Schwarz-Christoffel formula is used to give the conformal mapping from circular domain to triangle region, further by using elimination to change the composite boundary value problem into the Hilbert boundary value with discontinuous coefficients. By analytic continuation of the problem with discontinuous coefficients, the analytical solution of the composite boundary value problem is obtained.

关 键 词：Schwarz-Christoffel公式 椭圆函数 PLEMELJ公式 复合边值问题 

分 类 号：O175.8[理学—数学]