Determining the temperature from Cauchy data in corner domains

B. Tomas Johansson

doi:10.1504/IJCSM.2010.033930

Determining the temperature from Cauchy data in corner domains

B. Tomas Johansson

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the problem of reconstruction of the temperature from knowledge of the temperature and heat flux on a part of the boundary of a bounded planar domain containing corner points. An iterative method is proposed involving the solution of mixed boundary value problems for the heat equation (with time-dependent conductivity). These mixed problems are shown to be well-posed in a weighted Sobolev space.

Original language	English
Pages (from-to)	122-131
Number of pages	10
Journal	International Journal of Computing Science and Mathematics
Volume	3
Issue number	1/2
DOIs	https://doi.org/10.1504/IJCSM.2010.033930
Publication status	Published - 2010

Keywords

Cauchy problem
corner domains
heat equations
ill-posed
iterative regularisation
weighted Sobolev space
temperature reconstruction
heat flux
mixed boundary value
time-dependent conductivity

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10.1504/IJCSM.2010.033930

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title = "Determining the temperature from Cauchy data in corner domains",

abstract = "We consider the problem of reconstruction of the temperature from knowledge of the temperature and heat flux on a part of the boundary of a bounded planar domain containing corner points. An iterative method is proposed involving the solution of mixed boundary value problems for the heat equation (with time-dependent conductivity). These mixed problems are shown to be well-posed in a weighted Sobolev space.",

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AB - We consider the problem of reconstruction of the temperature from knowledge of the temperature and heat flux on a part of the boundary of a bounded planar domain containing corner points. An iterative method is proposed involving the solution of mixed boundary value problems for the heat equation (with time-dependent conductivity). These mixed problems are shown to be well-posed in a weighted Sobolev space.

KW - Cauchy problem

KW - corner domains

KW - heat equations

KW - ill-posed

KW - iterative regularisation

KW - weighted Sobolev space

KW - temperature reconstruction

KW - heat flux

KW - mixed boundary value

KW - time-dependent conductivity

UR - http://www.inderscience.com/info/inarticle.php?artid=33930

U2 - 10.1504/IJCSM.2010.033930

DO - 10.1504/IJCSM.2010.033930

M3 - Article

SN - 1752-5055

VL - 3

SP - 122

EP - 131

JO - International Journal of Computing Science and Mathematics

JF - International Journal of Computing Science and Mathematics

IS - 1/2

ER -

Determining the temperature from Cauchy data in corner domains

Abstract

Keywords

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