THE DIRICHLET-NEUMANN PROBLEM FOR THE DISSIPATIVE HELMHOLTZ EQUATION IN A 2-D CRACKED DOMAIN WITH THE NEUMANN CONDITION ON CRACKS

被引：2

作者：

Krutitskii, P. A. ^{[1
]}

Kolybasova, V. V. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Fac Phys, Dept Math, Moscow 119899, Russia

来源：

TSUKUBA JOURNAL OF MATHEMATICS | 2006年 / 30卷 / 01期

关键词：

D O I：

10.21099/tkbjm/1496165031

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Dirichlet-Neumann problem for the dissipative Helmholtz equation in a connected plane region bounded by closed curves and open arcs (cuts) is studied. The Dirichlet condition is specified on the closed curves, while the Neumann condition is specified on the cuts. The existence of a classical solution is proved by potential theory. The problem is reduced to a Fredholm equation of the second kind, which is uniquely solvable. An integral representation for the solution of the problem is obtained. Our approach holds for both interior and exterior domains.

引用

页码：103 / 129

页数：27

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