An iterative method for a Cauchy problem for the heat equation

Tomas Johansson

doi:10.1093/imamat/hxh093

An iterative method for a Cauchy problem for the heat equation

Tomas Johansson

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

Abstract

An iterative method for reconstruction of the solution to a parabolic initial boundary value problem of second order from Cauchy data is presented. The data are given on a part of the boundary. At each iteration step, a series of well-posed mixed boundary value problems are solved for the parabolic operator and its adjoint. The convergence proof of this method in a weighted L²-space is included.

Original language	English
Pages (from-to)	262-286
Number of pages	25
Journal	IMA Journal of Applied Mathematics
Volume	71
Issue number	2
Early online date	10 Jun 2005
DOIs	https://doi.org/10.1093/imamat/hxh093
Publication status	Published - Apr 2006

Keywords

cauchy problem
heat equation
iterative regularization method
mixed problem
weighted Sobolev space

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10.1093/imamat/hxh093

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title = "An iterative method for a Cauchy problem for the heat equation",

abstract = "An iterative method for reconstruction of the solution to a parabolic initial boundary value problem of second order from Cauchy data is presented. The data are given on a part of the boundary. At each iteration step, a series of well-posed mixed boundary value problems are solved for the parabolic operator and its adjoint. The convergence proof of this method in a weighted L2-space is included.",

keywords = "cauchy problem, heat equation , iterative regularization method, mixed problem, weighted Sobolev space",

author = "Tomas Johansson",

year = "2006",

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AB - An iterative method for reconstruction of the solution to a parabolic initial boundary value problem of second order from Cauchy data is presented. The data are given on a part of the boundary. At each iteration step, a series of well-posed mixed boundary value problems are solved for the parabolic operator and its adjoint. The convergence proof of this method in a weighted L2-space is included.

KW - cauchy problem

KW - heat equation

KW - iterative regularization method

KW - mixed problem

KW - weighted Sobolev space

UR - http://imamat.oxfordjournals.org/content/71/2/262

U2 - 10.1093/imamat/hxh093

DO - 10.1093/imamat/hxh093

M3 - Article

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VL - 71

SP - 262

EP - 286

JO - IMA Journal of Applied Mathematics

JF - IMA Journal of Applied Mathematics

IS - 2

ER -

An iterative method for a Cauchy problem for the heat equation

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