Asymptotic Solutions of the Dirichlet Problem for the Heat Equation at a Characteristic Point
- The Dirichlet problem for the heat equation in a bounded domain aS, a"e (n+1) is characteristic because there are boundary points at which the boundary touches a characteristic hyperplane t = c, where c is a constant. For the first time, necessary and sufficient conditions on the boundary guaranteeing that the solution is continuous up to the characteristic point were established by Petrovskii (1934) under the assumption that the Dirichlet data are continuous. The appearance of Petrovskii's paper was stimulated by the existing interest to the investigation of general boundary-value problems for parabolic equations in bounded domains. We contribute to the study of this problem by finding a formal solution of the Dirichlet problem for the heat equation in a neighborhood of a cuspidal characteristic boundary point and analyzing its asymptotic behavior.
Author details: | Alexandra Viktorivna AntonioukORCiDGND, Oleg M. Kiselev, Nikolai Nikolaevich TarkhanovORCiDGND |
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DOI: | https://doi.org/10.1007/s11253-015-1038-8 |
ISSN: | 0041-5995 |
ISSN: | 1573-9376 |
Title of parent work (English): | Ukrainian mathematical journal |
Publisher: | Springer |
Place of publishing: | New York |
Publication type: | Article |
Language: | English |
Year of first publication: | 2015 |
Publication year: | 2015 |
Release date: | 2017/03/27 |
Volume: | 66 |
Issue: | 10 |
Number of pages: | 20 |
First page: | 1455 |
Last Page: | 1474 |
Funding institution: | Alexander von Humboldt Foundation; National Academy of Sciences of Ukraine under Ukrainian National Academy of Sciences [01-01-12]; National Academy of Sciences of Ukraine under Russian Foundation for Fundamental Research [01-01-12]; Russian Foundation for Fundamental Research [11-01-91330-NNIO_a]; German Research Society (DFG) [TA 289/4-2] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |