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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
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
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
Linking options:
https://www.mathnet.ru/eng/sm7567https://doi.org/10.1070/SM2010v201n07ABEH004100 https://www.mathnet.ru/eng/sm/v201/i7/p67
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Abstract page: | 770 | Russian version PDF: | 254 | English version PDF: | 29 | References: | 90 | First page: | 23 |
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