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A stability estimate for a Cauchy problem for an elliptic partial differential equation
Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap.ORCID-id: 0000-0003-2281-856X
Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap.
2005 (engelsk)Inngår i: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 21, nr 5, s. 1643-1653Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

A two-dimensional inverse steady state heat conduction problem in the unit square is considered. Cauchy data are given for y ≤ 0, and boundary data are for x ≤ 0 and x ≤ 1. The elliptic operator is self-adjoint with non-constant, smooth coefficients. The solution for y ≤ 1 is sought. This Cauchy problem is ill-posed in an L2-setting. A stability functional is defined, for which a differential inequality is derived. Using this inequality a stability result of Hölder type is proved. It is demonstrated explicitly how the stability depends on the smoothness of the coefficients. The results can also be used for rectangle-like regions that can be mapped conformally onto a rectangle. © 2005 IOP Publishing Ltd.

sted, utgiver, år, opplag, sider
2005. Vol. 21, nr 5, s. 1643-1653
Emneord [en]
Cauchy problem, elliptic equation, heat conduction, inverse problem
HSV kategori
Identifikatorer
URN: urn:nbn:se:liu:diva-29345DOI: 10.1088/0266-5611/21/5/008Lokal ID: 14667OAI: oai:DiVA.org:liu-29345DiVA, id: diva2:250157
Tilgjengelig fra: 2009-10-09 Laget: 2009-10-09 Sist oppdatert: 2017-12-13

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Forlagets fullteksthttp://www.iop.org/EJ/abstract/0266-5611/21/5/008/

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