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 Mat. Sb., 2012, Volume 203, Number 4, Pages 131–160 (Mi msb7744)

The Cauchy problem for a quasilinear parabolic equation with gradient absorption

V. A. Markasheva, A. F. Tedeev

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences

Abstract: The qualitative properties of solutions to the Cauchy problem for a degenerate parabolic equation containing a nonlinear operator of Baouendi-Grushin type and with gradient absorption whose density depends on time, as well as the space variables, are investigated. Bounds for the diameter of the support of the solution which are sharp with respect to time are obtained, together with its maximum. A condition which determines whether or not the phenomenon of decay to zero of the total mass of the solution occurs is discovered.
Bibliography: 35 titles.

Keywords: operator of Baouendi-Grushin type, quasilinear parabolic equation, gradient absorption, decay of the total mass of a solution, estimate for the support of the solution.
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DOI: https://doi.org/10.4213/sm7744

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English version:
Sbornik: Mathematics, 2012, 203:4, 581–611

Bibliographic databases:

UDC: 517.946
MSC: Primary 35K59; Secondary 35R03
Received: 26.05.2010 and 26.08.2011

Citation: V. A. Markasheva, A. F. Tedeev, “The Cauchy problem for a quasilinear parabolic equation with gradient absorption”, Mat. Sb., 203:4 (2012), 131–160; Sb. Math., 203:4 (2012), 581–611

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb7744
• https://doi.org/10.4213/sm7744
• http://mi.mathnet.ru/eng/msb/v203/i4/p131

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This publication is cited in the following articles:
1. Anh Cung The, Tuyet Le Thi, “Strong solutions to a strongly degenerate semilinear parabolic equation”, Vietnam J. Math., 41:2 (2013), 217–232
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
4. Skrypnik I.I., Tedeev A.F., “Decay of the Mass of the Solution to the Cauchy Problem of the Degenerate Parabolic Equation With Nonlinear Potential”, Complex Var. Elliptic Equ., 63:1 (2018), 90–115
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