Boundary Value Problems For The Partial Differential Equations In Quaternionic Analysis

Abstract:In this paper, by using methods from complex analysis and quaternionic analysis,we investigate the initial-boundary value problems for the Maxwell equations and the Haseman boundary value problems for the hyperbolic type equations of first order in quaternion analysis.This paper consists of two chapters.In chapter one,on the basis of the text[42],by using methods from complex analysis and quaternionic analysis, we investigate an initial-boundary value problem for the Maxwell equations when the magnetic monopole is exist, and obtain the general solutions and solvable conditions of the problem respectively in different cases.In chapter two,on the basis of the text[39,57],we investigated the Haseman boundary value problems for the hyperbolic type equations of first order (i(?)+j(?))(f1+kf2)=0in the commutative quaternion space,and obtain the integral representation of general solutions.