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Sbornik: Mathematics, 2013, Volume 204, Issue 3, Pages 383–410
DOI: https://doi.org/10.1070/SM2013v204n03ABEH004305 (Mi sm8121) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Initial evolution of supports of solutions of quasilinear parabolic equations with degenerate absorption potential

E. V. Stepanovaa, A. E. Shishkovab

a Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk
b Donetsk National University, Ukraine
English version PDF (556 kB) Citations (3)
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DOI: https://doi.org/10.1070/SM2013v204n03ABEH004305
Abstract: The propagation of supports of solutions of second-order quasilinear parabolic equations is studied; the equations are of the type of nonstationary diffusion, having semilinear absorption with an absorption potential which degenerates on the initial plane. We find sufficient conditions, which are sharp in a certain sense, on the relationship between the boundary regime and the type of degeneration of the potential to ensure the strong localization of solutions. We also establish a weak localization of solutions for an arbitrary potential which degenerates only on the initial plane.
Bibliography: 12 titles.
Keywords: quasilinear parabolic equations, absorption potential, strong localization of solutions, weak localization of solutions, energy method.
Received: 22.03.2012 and 03.08.2012
Russian version:
Matematicheskii Sbornik, 2013, Volume 204, Number 3, Pages 79–106
DOI: https://doi.org/10.4213/sm8121
Bibliographic databases:
Document Type: Article
UDC: 517.957
MSC: Primary 35K65; Secondary 35B40, 35K55
Language: English
Original paper language: Russian
Citation: E. V. Stepanova, A. E. Shishkov, “Initial evolution of supports of solutions of quasilinear parabolic equations with degenerate absorption potential”, Mat. Sb., 204:3 (2013), 79–106; Sb. Math., 204:3 (2013), 383–410
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v204/i3/p79
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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