Rothe method for a mixed problem with an integral condition for the two-dimensional diffusion equation
type: Item
instance of: scholarly article
title: Rothe method for a mixed problem with an integral condition for the two-dimensional diffusion equation
zbMATH Open document ID: 1065.35026
DOI: 10.1155/S1085337503305019
author: Nabil Merazga
author: Abdelfatah Bouziani
published in: Abstract and Applied Analysis
publication date: 2005-04-29T00:00:00Z
full work available at URL: https://eudml.org/doc/51403
review text: The authors consider a two-dimensional heat equation in the unit square along with Neumann-type boundary conditions containing, on one side, an unknown function of \(t\). At the same time, the integral over the unit square of the solution is prescribed. The authors show that a related one-dimensional problem concerning the integral of the solution with respect to only one of the variables can be solved uniquely by the Rothe method, and they show stability and convergence results in corresponding function spaces.
reviewed by: Gisbert Stoyan
Mathematics Subject Classification ID: 35A35
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 65M12
zbMATH DE Number: 2163622
zbMATH Keywords: non-standard boundary condition
zbMATH Keywords: uniqueness
zbMATH Keywords: stability and convergence
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2163622