Zhang Peng. The Analytical Solution for Helmholtz Boundary Problem in Non Horizontally Stratified Domains[J]. Applied Mathematics and Mechanics, 1989, 10(12): 1077-1088.
 Citation: Zhang Peng. The Analytical Solution for Helmholtz Boundary Problem in Non Horizontally Stratified Domains[J]. Applied Mathematics and Mechanics, 1989, 10(12): 1077-1088.

# The Analytical Solution for Helmholtz Boundary Problem in Non Horizontally Stratified Domains

• Publish Date: 1989-12-15
• There are N domains Dj(j=0,1,...,N-1) of different physical parameters in the whole space and their interfaces Sj,i+1 are non-horizontally smooth curved surfaces. The following boundary problem is called Hclinholiz boundary problem:
2H(j)+KjH(j)=0 (j=0,1,…,N-1)
(H(0)-H(1))S0.1=δ(S) (δ(S):generalized function)
(H(1)-H(i+1))Sj,j+1=0 (j=0,1,…,N-2)
The analytical solution of the above problem is given in this paper.
•  [1] Голузин Г.М.,Геомеmрuческая Теорuя Функчuu Комnлелсно Переменноiо,Гостехиздат(1952) [2] Векуа И.Н.,Нобые Меmобы Рещенuя Злunmuческuх Урабненuu,Гпстехиздат(1948) [3] Мусхелишвили Н.И.,Сuнчмярные Инmеiралыные Урабненuя,Физматтнз(1962) [4] Gilbert,R.P.,Function Theoretic Methods in Partial Differential Equation,The Academic Press(1969). [5] 路见可,《解析画数边值问题》,上海科学技术出版社(1987). [6] Conway,John B.,Function of One Comples Variable,2nd ed.,Springer-Verlag Press,New York(1978). [7] Wait J.R.,Fields of a line current source over a stratified conductor,Appl.Sci.Res.,Sec.B.,3(1953),1-15. [8] Gordon,A.N.,The field indueed by an oscillating magnetic dipole outside a semi-infinite conductor,Mech.and App.Math.,4(1951),106-115.

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