A Fourier method for initial value problems with mixed boundary conditions
type: Item
instance of: scholarly article
title: A Fourier method for initial value problems with mixed boundary conditions
zbMATH Open document ID: 0635.65121
DOI: 10.1016/0898-1221(87)90152-0
author: M. G. El-Sheikh
author: Ulrich Eckhardt
publication date: 1987-01-01T00:00:00Z
review text: The classical heat equation, written in polar coordinates (r,\(\theta)\) is considered in the unit circle. At the arc \(r=1\), \(\theta\in (-c,c)\) heat flux is prescribed whereas at the complementary arc temperature does not change with time. Initial temperature is also given. The authors present in detail the analysis of obtaining the solution in form of a series containing trigonometric and Bessel functions in the case of time- independent heat flux. Actually, they derive such a series for the difference of the stationary and the transient solution. After discussing a few concrete examples they describe how the case of time-dependent flux can be treated by aid of Duhamel's principle.
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 4035072
zbMATH Keywords: Fourier method
zbMATH Keywords: heat equation
zbMATH Keywords: polar coordinates
zbMATH Keywords: series containing trigonometric and Bessel functions
zbMATH Keywords: Duhamel's principle
reviewed by: Rudolf Gorenflo
MaRDI profile type: Publication
full work available at URL: 0898-1221(87)90152-0
OpenAlex ID: W1989238062
cites work: A Note on some Mixed Boundary Value Problems for the Heat Equation
cites work: Q5820804
cites work: Q5327757
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4035072