Note on a boundary value problem of Poisson's equation
type: Item
instance of: scholarly article
title: Note on a boundary value problem of Poisson's equation
zbMATH Open document ID: 0832.31002
DOI: 10.1007/BF02663891
author: Chaokeng Feng
author: Lizhi Hsu
author: Hongquan Yu
published in: Applied Mathematics. Series B (English Edition)
publication date: 1996-03-05T00:00:00Z
review text: The boundary value problem of Poisson's equation in the half-plane \(- \infty< x<\infty\), \(y>0\), \(\Delta \varphi= Q(x, y)\) and \(\varphi (x, 0)= f(x)\) is solved in an integral form using Green's function. For some source functions \(Q(x, y)\) these integrals become difficult to evaluate. In such cases, the similarity method of differential equations to evaluate analytically these integrals can be tried. By considering a special class of functions \(Q(x, y)\), the authors show in this note that the similarity analysis is reliable in this context.
Mathematics Subject Classification ID: 31A30
Mathematics Subject Classification ID: 31A25
Mathematics Subject Classification ID: 35C05
zbMATH DE Number: 763879
zbMATH Keywords: similarity analysis
zbMATH Keywords: Green's function
zbMATH Keywords: Poisson's equation
reviewed by: Victor Anandam
MaRDI profile type: Publication
cites work: Nonlinear partial differential equations in engineering. Vol. II
cites work: Similarity methods for differential equations
cites work: Q3786804
description: scientific article; zbMATH DE number 763879