On the solvability on the spectrum of Fredholm boundary integral equations of the first kind for the three-dimensional transmission problem-Reference-Cited by-同舟云学术

On the solvability on the spectrum of Fredholm boundary integral equations of the first kind for the three-dimensional transmission problem

Published:2024-02-15 Issue:2 Volume:60 Page:211-223
ISSN:0374-0641
Container-title:Дифференциальные уравнения
language:
Short-container-title:Differencialʹnye uravneniâ

Author:

Kashirin A. A.¹,Smagin S. I.¹

Affiliation:

1. Computer Center of Far Eastern Branch of RAS

Abstract

The paper considers two weakly singular Fredholm boundary integral equations of the first kind, to each of which the three-dimensional Helmholtz transmission problem can be reduced. The properties of these equations are studied on spectra, where they are ill-posed. For the first equation, it is shown that if its solution exists on the spectrum, it allows us to find a solution to the transmission problem. The second equation in this case always has infinitely many solutions, only one of which gives a solution to the transmission problem. The interpolation method for finding approximate solutions of the considered integral equations and the transmission problem is discussed.

Publisher

The Russian Academy of Sciences

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