Boundary-value problems for Helmholtz equations in an angular domain. I

Authors

  • Yu. K. Podlipenko

Abstract

The boundary-value problems are investigated that arise when studying the diffraction of acoustic waves on an infinite cylinder with cross-section of an arbitrary shape situated inside a wedge so that the axis of the cylinder is parallel to the edge of the wedge. The potential theory is worked out which enables one to reduce these boundary-value problems to integral equations on a one-dimensional contour — the boundary of the cross-section of this cylinder. The theorems on existence and uniqueness of solutions to the boundary-value problems and the corresponding integral equations are proved. For this case, a principle of limit absorption is established. Effective algorithms for calculating the kernels of the integral operators are constructed.

Published

25.03.1993

Issue

Section

Research articles

How to Cite

Podlipenko, Yu. K. “Boundary-Value Problems for Helmholtz Equations in an Angular Domain. I”. Ukrains’kyi Matematychnyi Zhurnal, vol. 45, no. 3, Mar. 1993, pp. 403–418, https://umj.imath.kiev.ua/index.php/umj/article/view/5823.