The Dirichlet Problem on Wave Propagation in a 2-D Exterior Cracked Domain with Compatibility Conditions at the Tips of the Cracks

被引：0

作者：

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

机构：

[1] KIAM, Moscow 125047, Russia

来源：

APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES | 2009年 / 1186卷

关键词：

Wave scattering by obstacles; Helmholtz equation; boundary value problem; potential theory; boundary integral equations; HELMHOLTZ-EQUATION; CUTS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Dirichlet problem for the 2-D Helmholtz equation in an exterior domain with cracks is studied. The compatibility conditions at the tips of the cracks are assumed. The existence of a unique classical solution is proved by potential theory. The integral representation for a solution is obtained. The problem is reduced to the Fredholm equation of the second kind and of index zero, which is uniquely solvable.

引用

页码：271 / 283

页数：13

共 12 条

[1] Gilbarg D., 1989, ELLIPTIC PARTIAL DIF
[2] Kantorovich LV, 1982, FUNCTIONAL ANAL
[3] Kolmogorov A. N., 1976, ELEMENTS FUNCTION TH
[4] Krein S. G., 1972, Functional Analysis
[5] The Dirichlet problem for the 2-D Helmholtz equation in a multiply connected domain with cuts
Krutitskii, PA
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1997, 77 (12): : 883 - 890
[6] KRUTITSKII PA, 1994, COMP MATH MATH PHYS+, V34, P1073
[7] On a uniquely solvable integral equation in a mixed Dirichlet-Neumann problem of acoustic scattering
Krutitskii, PA
[J]. QUARTERLY OF APPLIED MATHEMATICS, 2001, 59 (03) : 493 - 506
[8] MUSKHELISHILI NI, 1972, SINGULAR INTEGRAL EQ
[9] Smirnov V. I., 1964, COURSE HIGHER MATH, V4
[10] Tikhonov A.N., 1963, Equations of mathematical physics

← 1 2 →