Open AccessFinding the fundamental solution of the bi-axially symmetric Laplace–Beltrami equation using generalized shift operator
Author(s) -
R. M. Mavlyaviev,
Ilnur Garipov,
Elena Rashidovna Sadykova,
O. V. Razumova
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2052/1/012025
Subject(s) - laplace's equation , boundary value problem , axial symmetry , partial differential equation , mathematics , heat equation , mathematical analysis , elasticity (physics) , laplace transform , operator (biology) , method of fundamental solutions , physics , singular boundary method , geometry , boundary element method , finite element method , biochemistry , chemistry , repressor , gene , transcription factor , thermodynamics
Many physical processes are described by partial differential equations. The relevance of this study is due to the need to solve applied problems of quantum mechanics, the theory of elasticity, and heat capacity. In this paper, an equation is considered that describes the field created by a contour with two axes of symmetry. The purpose of the study is to find a fundamental solution to this equation, which can later be used when solving boundary value problems.