The Dirichlet problem for the heat equation in a bounded domain is characteristic, for there are boundary points at which the boundary touches a
characteristic hyperplane t = c, c being a constant. It was I.G. Petrovskii (1934) who first found necessary and sufficient conditions on the boundary which guarantee that the solution is continuous up to the characteristic
point, provided that the Dirichlet data are continuous. This paper initiated standing interest in studying general boundary value problems for parabolic equations in bounded domains. We contribute to the study by constructing a formal solution of the Dirichlet problem for the heat equation in a neighbourhood of a characteristic boundary point and showing its asymptotic character.
| Identifer | oai:union.ndltd.org:Potsdam/oai:kobv.de-opus-ubp:6198 |
| Date | January 2012 |
| Creators | Antoniouk, Alexandra, Kiselev, Oleg, Stepanenko, Vitaly, Tarkhanov, Nikolai |
| Publisher | Universität Potsdam, Mathematisch-Naturwissenschaftliche Fakultät. Institut für Mathematik |
| Source Sets | Potsdam University |
| Language | English |
| Detected Language | English |
| Type | Preprint |
| Format | application/pdf |
| Rights | http://opus.kobv.de/ubp/doku/urheberrecht.php |
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