
This article is cited in 2 scientific papers (total in 2 papers)
The properties of the solutions for Cauchy problem of nonlinear parabolic equations in nondivergent form with density
Jakhongir R. Raimbekov^{} ^{} National University of Uzbekistan, Yunus Abad17, 3/66, 10037,
Tashkent, Uzbekistan
Abstract:
We investigate the solutions for the following nonlinear degenerate parabolic equation in nondivergent form with density
$$
x^{n} \frac{\partial u}{\partial t} =u^{m} div(\nabla u^{p2} \nabla u).
$$
We discuss the properties, which are different from those for the equations in divergence form, thus generalizing various known results. Then getting a selfsimilar solution we show the asymptotic behavior of solutions at $t \to \infty$. Slow and fast diffusion cases are investigated. Finally, we present the results of some numerical experiments.
Keywords:
nonlinear degenerate parabolic equation, nondivergent form, selfsimilar solution, asymptotic behavior of solutions.
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UDC:
517.955.8 Received: 02.04.2014 Received in revised form: 15.10.2014 Accepted: 03.04.2014
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Jakhongir R. Raimbekov, “The properties of the solutions for Cauchy problem of nonlinear parabolic equations in nondivergent form with density”, J. Sib. Fed. Univ. Math. Phys., 8:2 (2015), 192–200
Citation in format AMSBIB
\Bibitem{Rai15}
\by Jakhongir~R.~Raimbekov
\paper The properties of the solutions for Cauchy problem of nonlinear parabolic equations in nondivergent form with density
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2015
\vol 8
\issue 2
\pages 192200
\mathnet{http://mi.mathnet.ru/jsfu421}
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This publication is cited in the following articles:

M. M. Aripov, A. S. Matyakubov, “Selfsimilar solutions of a crossdiffusion parabolic system with variable density: explicit estimates and asymptotic behaviour”, Nanosyst.Phys. Chem. Math., 8:1 (2017), 5–12

Mersaid M. Aripov, Jakhongir R. Raimbekov, “The critical curves of a doubly nonlinear parabolic equation in nondivergent form with a source and nonlinear boundary flux”, Zhurn. SFU. Ser. Matem. i fiz., 12:1 (2019), 112–124

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