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The Dirichlet Problem for the 2‐D Helmholtz Equation in a Multiply Connected Domain with Cuts
Author(s) -
Krutitskii P. A.
Publication year - 1997
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19970771202
Subject(s) - helmholtz equation , dirichlet problem , dissipative system , mathematics , fredholm integral equation , mathematical analysis , domain (mathematical analysis) , dirichlet distribution , plane (geometry) , dirichlet integral , dirichlet's principle , integral equation , physics , boundary value problem , geometry , quantum mechanics
The Dirichlet problem for the dissipative Helmholtz equation in a connected plane region with cuts is studied. The existence of a classical solution is proved by potential theory. The problem is reduced to a Fredholm equation of second kind, which is uniquely solvable.