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J. Sib. Fed. Univ. Math. Phys., 2013, Volume 6, Issue 2, Pages 157–167 (Mi jsfu307)  

This article is cited in 4 scientific papers (total in 4 papers)

To properties of solutions to reaction-diffusion equation with double nonlinearity with distributed parameters

Mersaid Aripova, Shakhlo A. Sadullaevab

a National University of Uzbekistan, Tashkent, Uzbekistan
b Tashkent University of Information Technologies, Tashkent, Uzbekistan

Abstract: The properties of solutions of self-similar and approximately self-similar system of the reaction-diffusion with double nonlinearity are investigated. The influence of numerical parameters to an evolution of the studied process is established. The existence of finite and quenching solutions is proved and their asymptotic behavior at the infinity is described. The condition of global solvability to the Cauchy problem, generalizing the results of other authors, is found. Knerr–Kersner type estimate for free boundary is obtained. The results of numerical experiments are enclosed.

Keywords: reaction-diffusion equation, double nonlinearity, free boundary.

Full text: PDF file (787 kB)
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UDC: 517.9
Received: 13.02.2013
Received in revised form: 27.02.2013
Accepted: 27.02.2013
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Citation: Mersaid Aripov, Shakhlo A. Sadullaeva, “To properties of solutions to reaction-diffusion equation with double nonlinearity with distributed parameters”, J. Sib. Fed. Univ. Math. Phys., 6:2 (2013), 157–167

Citation in format AMSBIB
\Bibitem{AriSad13}
\by Mersaid~Aripov, Shakhlo~A.~Sadullaeva
\paper To properties of solutions to reaction-diffusion equation with double nonlinearity with distributed parameters
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2013
\vol 6
\issue 2
\pages 157--167
\mathnet{http://mi.mathnet.ru/jsfu307}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Jakhongir R. Raimbekov, “The properties of the solutions for Cauchy problem of nonlinear parabolic equations in non-divergent form with density”, Zhurn. SFU. Ser. Matem. i fiz., 8:2 (2015), 192–200  mathnet
    2. Shahlo A. Sadullaeva, “Numerical investigation of solutions to a reaction-diffusion system with variable density”, Zhurn. SFU. Ser. Matem. i fiz., 9:1 (2016), 90–101  mathnet  crossref
    3. Z. R. Rakhmonov, A. I. Tillaev, “On the behavior of the solution of a nonlinear polytropic filtration problem with a source and multiple nonlinearities”, Nanosyst.-Phys. Chem. Math., 9:3 (2018), 323–329  crossref  isi
    4. Mersaid M. Aripov, Jakhongir R. Raimbekov, “The critical curves of a doubly nonlinear parabolic equation in non-divergent form with a source and nonlinear boundary flux”, Zhurn. SFU. Ser. Matem. i fiz., 12:1 (2019), 112–124  mathnet  crossref
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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