On the weak solution of a three-point boundary value problem for a class of parabolic equations with energy specification
type: Item
instance of: scholarly article
title: On the weak solution of a three-point boundary value problem for a class of parabolic equations with energy specification
zbMATH Open document ID: 1031.35051
DOI: 10.1155/S1085337503210010
author: Abdelfatah Bouziani
published in: Abstract and Applied Analysis
publication date: 2003-06-18T00:00:00Z
full work available at URL: https://eudml.org/doc/50576
review text: The author proves in weighted Sobolev spaces the existence, uniqueness, and continuous dependence of the weak solution of three-point boundary value problem for a class of linear and quasilinear parabolic equations with nonlocal condition in a domain with curved boundaries varying with respect to time. To this end the author uses a priori estimates technique. To investigate quasilinear problem the author combines an iterative process with results established for the linear case.
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 35B30
zbMATH DE Number: 1929978
zbMATH Keywords: quasilinear equations
zbMATH Keywords: weighted Sobolev spaces
zbMATH Keywords: iterative process
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
OpenAlex ID: W1970932335
description: scientific article; zbMATH DE number 1929978