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Matematicheskie Zametki, 2009, Volume 85, Issue 3, Pages 395–407
DOI: https://doi.org/10.4213/mzm4100 (Mi mzm4100) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Local and Global Estimates of the Solutions of the Cauchy Problem for Quasilinear Parabolic Equations with a Nonlinear Operator of Baouendi–Grushin Type

V. A. Markasheva, A. F. Tedeev

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences
Full-text PDF (517 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm4100
Abstract: In this paper, the qualitative properties of the solutions of the Cauchy problem for degenerate parabolic equations with a nonlinear operator of Baouendi–Grushin type are studied. Sharp local and global (with respect to the spatial and temporal variables) estimates of the solution are obtained. The property of the finiteness of the support of the solution is established.
Keywords: quasilinear parabolic equation, nonlinear operator, Cauchy problem, Carnot–Carathéodory space, Young's inequality, maximum principle.
Received: 16.03.2007
English version:
Mathematical Notes, 2009, Volume 85, Issue 3, Pages 385–396
DOI: https://doi.org/10.1134/S0001434609030092
Bibliographic databases:
UDC: 517.946
Language: Russian
Citation: V. A. Markasheva, A. F. Tedeev, “Local and Global Estimates of the Solutions of the Cauchy Problem for Quasilinear Parabolic Equations with a Nonlinear Operator of Baouendi–Grushin Type”, Mat. Zametki, 85:3 (2009), 395–407; Math. Notes, 85:3 (2009), 385–396
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    1. Anh Cung The, “Global attractor for a semilinear strongly degenerate parabolic equation on RN”, NoDEA Nonlinear Differential Equations Appl., 21:5 (2014), 663–678  crossref  mathscinet  zmath  isi  scopus
    2. Anh Cung The, Tuyet Le Thi, “On a semilinear strongly degenerate parabolic equation in an unbounded domain”, J. Math. Sci. Univ. Tokyo, 20:1 (2013), 91–113  mathscinet  zmath  isi
    3. Cung The Anh, Le Thi Tuyet, “Strong Solutions to a Strongly Degenerate Semilinear Parabolic Equation”, Viet J Math, 41:2 (2013), 217  crossref
    4. V. A. Markasheva, An. F. Tedeev, “The Cauchy problem for a quasilinear parabolic equation with gradient absorption”, Sb. Math., 203:4 (2012), 581–611  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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