Determining the temperature from Cauchy data in corner domains
type: Item
instance of: scholarly article
title: Determining the temperature from Cauchy data in corner domains
zbMATH Open document ID: 1206.80027
DOI: 10.1504/IJCSM.2010.033930
author: B. Tomas Johansson
published in: International Journal of Computing Science and Mathematics
publication date: 2010-08-17T00:00:00Z
review text: The paper is concerned with the analysis of the solvability of the problem to reconstruct the temperature in a plane domain containing corner points from the knowledge of the temperature and heat flux only on a portion of the boundary. The model is based on the classical linear heat equation with a smooth thermal coefficient. The solution procedure is an iterative scheme involving two mixed problems, one obtained from the original equations with the substitution of the Newman condition with a Dirichlet condition on the remaining part of the boundary, the other is its adjoint. The main result is the proof of solvability of the mixed problem in a weighted Sobolev space. The choice of the space is determined by the presence of singularity due to the corners and the mixed type of boundary conditions. The result generalizes the time depended case of a previous paper of the same author [\textit{T. Johansson} and \textit{L. Marin}, Inverse Probl. 23, No. 1, 357--372 (2007; Zbl 1119.35114)].
reviewed by: Vittorio Romano
Mathematics Subject Classification ID: 80M99
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 5771947
zbMATH Keywords: Cauchy problem
zbMATH Keywords: corner domain
zbMATH Keywords: heat equation
zbMATH Keywords: ill-posed
zbMATH Keywords: iterative regularisation
zbMATH Keywords: weighted Sobolev space
MaRDI profile type: Publication
full work available at URL: ijcsm.2010.033930
OpenAlex ID: W2037692837
description: scientific article; zbMATH DE number 5771947