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A uniqueness result for an overdetermined problem in non-linear parabolic potential theory
KTH, Superseded Departments, Mathematics.ORCID iD: 0000-0002-1316-7913
2004 (English)In: Potential Analysis, ISSN 0926-2601, E-ISSN 1572-929X, Vol. 21, no 4, 405-414 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we study the question of uniqueness for an inverse problem, arising in the (thermal) linear and/or non-linear potential theory. The overdetermined problem we shall study is represented by (div(\delu\(p-2)delu) - D(t)u - chi(Omega) + mu)u = 0, where supp(mu) subset of Omega subset of R-n x (0,infinity), 1 < p < infinity, mu is an element of L-infinity, and Omega boolean AND {t = tau} is bounded for tau > 0. The problem has applications in shape-recognition in underground water/oil recovery, subject to shape-change during time intervals. The particular case u greater than or equal to 0, D(t)u greater than or equal to 0, and p = 2, is an example of the well-known Stefan.

Place, publisher, year, edition, pages
2004. Vol. 21, no 4, 405-414 p.
Keyword [en]
uniqueness, parabolic potential theory
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-39784DOI: 10.1023/B:POTA.0000034328.18233.55ISI: 000222501900004Scopus ID: 2-s2.0-3242715223OAI: oai:DiVA.org:kth-39784DiVA: diva2:442164
Note
QC 20110920Available from: 2011-09-20 Created: 2011-09-12 Last updated: 2017-12-08Bibliographically approved

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Shahgholian, Henrik

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