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 Mat. Zametki, 2009, Volume 85, Issue 3, Pages 395–407 (Mi mz4100)

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

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

DOI: https://doi.org/10.4213/mzm4100

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English version:
Mathematical Notes, 2009, 85:3, 385–396

Bibliographic databases:

UDC: 517.946

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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• http://mi.mathnet.ru/eng/mz4100
• https://doi.org/10.4213/mzm4100
• http://mi.mathnet.ru/eng/mz/v85/i3/p395

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This publication is cited in the following articles:
1. V. A. Markasheva, A. F. Tedeev, “The Cauchy problem for a quasilinear parabolic equation with gradient absorption”, Sb. Math., 203:4 (2012), 581–611
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
3. Anh Cung The, “Global attractor for a semilinear strongly degenerate parabolic equation on $\mathbb R^N$”, NoDEA Nonlinear Differential Equations Appl., 21:5 (2014), 663–678
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