Tsukuba Journal of Mathematics

The Dirichlet-Neumann problem for the dissipative Helmholtz equation in a 2-D cracked domain with the Neumann condition on cracks

V. V. Kolybasova and P. A. Krutitskii

Full-text: Open access

Abstract

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.

Article information

Source
Tsukuba J. Math., Volume 30, Number 1 (2006), 103-129.

Dates
First available in Project Euclid: 30 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1496165031

Digital Object Identifier
doi:10.21099/tkbjm/1496165031

Mathematical Reviews number (MathSciNet)
MR2248286

Zentralblatt MATH identifier
1210.35035

Citation

Krutitskii, P. A.; Kolybasova, V. V. The Dirichlet-Neumann problem for the dissipative Helmholtz equation in a 2-D cracked domain with the Neumann condition on cracks. Tsukuba J. Math. 30 (2006), no. 1, 103--129. doi:10.21099/tkbjm/1496165031. https://projecteuclid.org/euclid.tkbjm/1496165031


Export citation