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

  • 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
How to Cite
PodlipenkoY. 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.
Section
Research articles