Properties of solutions of the Dirichlet problem for the Helmholtz equation in a two-dimensional domain with cuts

DOI10.1134/S0012266107090030zbMath1181.35052OpenAlexW2046035222WikidataQ115253313 ScholiaQ115253313MaRDI QIDQ1033639

P. A. Krutitskii

Publication date: 6 November 2009

Published in: Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0012266107090030

zbMATH Keywords

weak solutionDirichlet problemsintegral representationHelmholtz equationclassical solutiondomains with cuts

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Integral representations of solutions to PDEs (35C15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (1)

Boundary Galerkin method of a skew-derivative problem in the exterior of an open arc based on Chebyshev polynomials

Cites Work

• The Dirichlet-Neumann problem for the dissipative Helmholtz equation in a 2-D cracked domain with the Neumann condition on cracks
• The Dirichlet problem for the dissipative Helmholtz equation in a plane domain bounded by closed and open curves
• Neumann's problem for the Helmholtz equation outside cuts in the plane
• The Dirichlet Problem for the 2‐D Helmholtz Equation in a Multiply Connected Domain with Cuts
• Wave propagation in a 2-D external domain bounded by closed and open curves
• Wave propagation in a 2-D external domain with cuts
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