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A nonstandard Cauchy problem for the heat equation

  • We consider a Cauchy problem for the heat equation in a cylinder X x (0,T) over a domain X in the n-dimensional space with data on a strip lying on the lateral surface. The strip is of the form S x (0,T), where S is an open subset of the boundary of X. The problem is ill-posed. Under natural restrictions on the configuration of S we derive an explicit formula for solutions of this problem.

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Metadaten
Author:K. O. Makhmudov, O. I. Makhmudov, Nikolai Nikolaevich TarkhanovORCiDGND
URN:urn:nbn:de:kobv:517-opus4-83830
ISSN:2193-6943 (online)
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Potsdam (4 (2015)11)
Publisher:Universitätsverlag Potsdam
Place of publication:Potsdam
Document Type:Preprint
Language:English
Year of first Publication:2015
Year of Completion:2015
Publishing Institution:Universität Potsdam
Publishing Institution:Universitätsverlag Potsdam
Release Date:2015/11/17
Tag:Carleman formulas; Cauchy problem; heat equation
Volume:4
Issue:11
Pagenumber:14
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K05 Heat equation
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K15 Initial value problems for second-order parabolic equations
Collections:Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2015
Publication Way:Universitätsverlag Potsdam
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht