The method of axisymmetric generalized analytical functions in the analysis of dynamic processes
type: Item
instance of: scholarly article
title: The method of axisymmetric generalized analytical functions in the analysis of dynamic processes
zbMATH Open document ID: 0754.30035
DOI: 10.1016/0021-8928(91)90083-7
published in: Journal of Applied Mathematics and Mechanics
publication date: 1992-09-27T00:00:00Z
review text: Let \(D\subset\mathbb{C}\) be a bounded domain with boundary \(\partial D\) and \(f(x,y)=0\) for \(z:=x+iy\in\partial D\), where \(f\) is a harmonic function in \(D\). The author introduces an axisymmetric generalized analytic function \(w=\varphi+i\psi/f\) (i.e. complex potential for axisymmetric field) by the system \[ {\partial\varphi\over\partial x}={1\over f}{\partial\psi\over\partial y},\quad{\partial\varphi\over\partial y}=- {1\over f}{\partial\psi\over\partial x}\quad\text{for } z\in D. \] He applies Polojii's theory of \(p\)-analytic functions (\textit{N. Polojii} [Theory and applications of \(p\)-analytic and \((p,q)\)-analytic functions (Russian) (Naukova Dumka) (1973; Zbl 0257.30040)]) and obtains a generalized Cauchy theorem, Morera's theorem, etc. Finally, some applications to three-dimensional boundary problems in a piecewise- homogeneous medium are given.
Mathematics Subject Classification ID: 30G20
Mathematics Subject Classification ID: 76S05
zbMATH DE Number: 58599
zbMATH Keywords: harmonic function
zbMATH Keywords: complex potential for azisymmetric field
zbMATH Keywords: Polojii's theory
zbMATH Keywords: \(p\)-analytic functions
zbMATH Keywords: boundary problems
zbMATH Keywords: piecewise-homogeneous medium
author: V. F. Piven'
MaRDI profile type: Publication
full work available at URL: 0021-8928(91)90083-7
OpenAlex ID: W2085346876
cites work: Q3329690
cites work: Q4040553
cites work: Q5673166
cites work: Q3256015
cites work: Q5511531
cites work: Q5845357
cites work: Q3264796
description: scientific article; zbMATH DE number 58599