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Sbornik: Mathematics, 2010, Volume 201, Issue 7, Pages 999–1028
DOI: https://doi.org/10.1070/SM2010v201n07ABEH004100
(Mi sm7567)
 

This article is cited in 7 scientific papers (total in 7 papers)

The solvability of the first initial-boundary problem for parabolic and degenerate parabolic equations in domains with a conical point

S. P. Degtyarev

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences
References:
Abstract: The first initial-boundary problem for second-order parabolic and degenerate parabolic equations is investigated in a domain with a conical or angular point. The means of attack is already known and uses weighted classes of smooth or integrable functions. Sufficient conditions for a unique solution to exist and for coercive estimates for the solution to be obtained are formulated in terms of the angular measure of the solid angle and the exponent of the weight. It is also shown that if these conditions fail to hold, then the parabolic problem has elliptic properties, that is, it can have a nonzero kernel or can be nonsolvable, and, in the latter case, it is not even a Fredholm problem. A parabolic equation and an equation with some degeneracy or a singularity at a conical point are considered.
Bibliography: 49 titles.
Keywords: parabolic equation, irregular domain, coercive estimate, spectral properties.
Received: 08.04.2009 and 25.11.2009
Russian version:
Matematicheskii Sbornik, 2010, Volume 201, Number 7, Pages 67–98
DOI: https://doi.org/10.4213/sm7567
Bibliographic databases:
Document Type: Article
UDC: 517.954+517.956.8+517.956.4
MSC: Primary 35K20; Secondary 35K65
Language: English
Original paper language: Russian
Citation: S. P. Degtyarev, “The solvability of the first initial-boundary problem for parabolic and degenerate parabolic equations in domains with a conical point”, Mat. Sb., 201:7 (2010), 67–98; Sb. Math., 201:7 (2010), 999–1028
Citation in format AMSBIB
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  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
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    Abstract page:770
    Russian version PDF:254
    English version PDF:29
    References:90
    First page:23
     
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