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

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

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.

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UDC: 517.9
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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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
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
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
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
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