On the selfsimilar solutions of a diffusion convection equation
type: Item
instance of: scholarly article
title: On the selfsimilar solutions of a diffusion convection equation
zbMATH Open document ID: 1019.34020
author: Abdelilah Gmira
author: Benyouness Bettioui
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2002-12-01T00:00:00Z
review text: The question on finding of radial solutions to a certain degenerate elliptic equation on \(\mathbb{R}^N\), \(N\geq 1\), is reduced to the question on the existence of solutions to the boundary value problem \[ (|u'|^{p-2}u')'+\frac{N-1}{r}|u'|^{p-2}u'+\varepsilon|u'|^q+\beta ru'+\alpha u=0, \;r>0, \quad u(0)=\mu,\;u'(0)=0, \] where \(p>2\), \(q\geq 1\), \(\varepsilon=\pm 1\), and \(\alpha\), \(\beta\) and \(\mu\) are fixed parameters. An existence and uniqueness theorem for the above-mentioned problem is proved. The existence and asymptotic behaviour of positive solutions to the considered problem is studied.
reviewed by: Robert Hakl
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 34B18
zbMATH DE Number: 1837010
zbMATH Keywords: selfsimilar solutions
zbMATH Keywords: diffusion convection equation
zbMATH Keywords: degenerate elliptic equation
zbMATH Keywords: existence
zbMATH Keywords: solutions
zbMATH Keywords: uniqueness
MaRDI profile type: Publication
full work available at URL: s00030-002-8128-7
OpenAlex ID: W2024985363
DOI: 10.1007/S00030-002-8128-7
description: scientific article; zbMATH DE number 1837010