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An alternating method for the stationary Stokes system
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
Linköping University, The Institute of Technology. Linköping University, Department of Science and Technology.
2006 (English)In: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, Vol. 86, no 4, 268-280 p.Article in journal (Refereed) Published
Abstract [en]

An alternating procedure for solving a Cauchy problem for the stationary Stokes system is presented. A convergence proof of this procedure and numerical results are included. © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Place, publisher, year, edition, pages
2006. Vol. 86, no 4, 268-280 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-41016DOI: 10.1002/zamm.200410238Local ID: 54933OAI: oai:DiVA.org:liu-41016DiVA: diva2:261866
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2017-12-13
In thesis
1. Reconstruction of flow and temperature from boundary data
Open this publication in new window or tab >>Reconstruction of flow and temperature from boundary data
2003 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis, we study Cauchy problems for elliptic and parabolic equations. These include the stationary Stokes system and the heat equation. Data are given on a part of the boundary of a bounded domain. The aim is to reconstruct the solution from these data. These problems are ill-posed in the sense of J. Hadamard.

We propose iterative regularization methods, which require solving of a sequence of well-posed boundary value problems for the same operator. Methods based on this idea were _rst proposed by V. A. Kozlov and V. G. Maz'ya for a certain class of equations which do not include the above problems. Regularizing character is proved and stopping rules are proposed.

The regularizing character for the heat equation is proved in a certain weighted L2 space. In each iteration the Zaremba problem for the heat equation is solved. We also prove well-posedness of this problem in a weighted Sobolev space. This result is of independent interest and is presented as a separate paper.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2003. 13 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 832
Keyword
Partiella differentialekvationer, Operatorteori
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-140145 (URN)91-7373-682-1 (ISBN)
Public defence
2003-10-24, TP2, Täppan, Campus Norrköping, Norrköping, 10:15 (English)
Opponent
Supervisors
Available from: 2017-08-31 Created: 2017-08-31 Last updated: 2017-09-08Bibliographically approved

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Kozlov, VladimirBaravdish, George

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