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.

Metadaten
Author details:	K. O. Makhmudov, O. I. Makhmudov, Nikolai Nikolaevich Tarkhanov ORCiD GND
URN:	urn:nbn:de:kobv:517-opus4-83830
ISSN:	2193-6943
Publication series (Volume number):	Preprints des Instituts für Mathematik der Universität Potsdam (4 (2015)11)
Publisher:	Universitätsverlag Potsdam
Place of publishing:	Potsdam
Publication type:	Preprint
Language:	English
Year of first publication:	2015
Publication year:	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
Number of pages:	14
Organizational units:	Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC 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
Collection(s):	Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2015
Publishing method:	Universitätsverlag Potsdam
License (German):	Keine öffentliche Lizenz: Unter Urheberrechtsschutz