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.
Citation:
V. A. Markasheva, An. F. Tedeev, “The Cauchy problem for a quasilinear parabolic equation with gradient absorption”, Sb. Math., 203:4 (2012), 581–611
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\paper The Cauchy problem for a~quasilinear parabolic equation with gradient absorption
\jour Sb. Math.
\yr 2012
\vol 203
\issue 4
\pages 581--611
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https://www.mathnet.ru/eng/sm7744
https://doi.org/10.1070/SM2012v203n04ABEH004236
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This publication is cited in the following 4 articles:
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
Anh Cung The, “Global attractor for a semilinear strongly degenerate parabolic equation on RN”, NoDEA Nonlinear Differential Equations Appl., 21:5 (2014), 663–678
Anh Cung The, Tuyet Le Thi, “Strong solutions to a strongly degenerate semilinear parabolic equation”, Vietnam J. Math., 41:2 (2013), 217–232
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
Citation in format AMSBIB
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