一类一阶四元双曲方程在双圆柱区域上的一个Riemann-hilbert边值问题  

A Riemann-hilbert boundary value problem for a first order hyperbolic equation with four variables

作　　者：张位全[1] 李觉友[2] 曾纯一[3] 

机构地区：[1]广东医学院数学教研室,广东东莞523808 [2]重庆师范大学数学与计算机科学学院,重庆400047 [3]西南民族大学预科教育学院,成都6140041

出　　处：《西南民族大学学报（自然科学版）》2008年第4期656-659,共4页Journal of Southwest Minzu University(Natural Science Edition)

摘　　要：为考察高维双曲方程的边值问题,本文引进可换四元数空间,并在此空间中讨论了可换四元数代数中一类一阶双曲方程的Riemann-Hilbert边值问题,我们获得了在指标非负的情况下唯一解的一般形式,以及在有指标小于零时代不同情况下Riemann-Hilbert边值问题的可解条件.In this paper, we study thee Riemann-Hilbert boundary value problem on the unit disk for a class of first order hyperbolic equation in commutative quaternion algebra. By changing this problem into a boundary value problem for a second order homogeneous equation and another boundary value problem for a inhomogeneous Cauchy -Riemann system, we obtain the general solution in the case of nonnegative exponents and the solvable condition of the problem in the case of negative exponents existing.

关 键 词：可换四元数 RIEMANN-HILBERT边值问题 双曲方程 

分 类 号：O241.7[理学—计算数学]