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

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.