The Neumann problem for the 2-D Helmholtz equation in a domain, bounded by closed and open curvesReport as inadecuate




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International Journal of Mathematics and Mathematical Sciences - Volume 21 1998, Issue 2, Pages 209-216

Dept. of Mathematics, Faculty of Physics, Moscow State University, Moscow 119899, Russia

Received 23 September 1996; Revised 17 April 1997

Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The Neumann problem for the dissipative Helmholtz equation in a connectedplane region bounded by closed and open curves is studied. The existence of classical solution isproved by potential theory. The problem is reduced to the Fredholm equation of the second kind,which is uniquely solvable. Our approach holds for both internal and external domains.





Author: P. A. Krutitskii

Source: https://www.hindawi.com/



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