This article is cited in 8 scientific papers (total in 8 papers)
On the properties of solutions of multidimensional nonlinear filtration problem with variable density and nonlocal boundary condition in the case of fast diffusion
Abstract:
The conditions of global existence of solutions of a nonlinear filtration problem in an inhomogeneous medium are investigated in this paper. Various techniques such as the method of standard equations, self-similar analysis and the comparison principle are used to obtain results. The influence of inhomogeneous medium on the evolution process is analyzed. The critical global existence exponent and the critical Fujita exponent are obtained. Asymptotic behavior of solutions in the case of the global solvability is established.
Received: 30.08.2015 Received in revised form: 04.12.2015 Accepted: 12.01.2016
Bibliographic databases:
Document Type:
Article
UDC:517.957
Language: English
Citation:
Zafar R. Rakhmonov, “On the properties of solutions of multidimensional nonlinear filtration problem with variable density and nonlocal boundary condition in the case of fast diffusion”, J. Sib. Fed. Univ. Math. Phys., 9:2 (2016), 225–234
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\by Zafar~R.~Rakhmonov
\paper On the properties of solutions of multidimensional nonlinear filtration problem with variable density and nonlocal boundary condition in the case of fast diffusion
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2016
\vol 9
\issue 2
\pages 225--234
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\crossref{https://doi.org/10.17516/1997-1397-2016-9-2-225-234}
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https://www.mathnet.ru/eng/jsfu480
https://www.mathnet.ru/eng/jsfu/v9/i2/p225
This publication is cited in the following 8 articles:
Mersaid Aripov, Odiljon Atabaev, “ON THE BLOWING-UP OF SOLUTIONS OF ONE DEGENERATE CROSS-WISE SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS”, VOGUMFT, 2023, no. 2(3), 158
A. A. Alimov, Z. R. Rakhmonov, “Globalnye resheniya i resheniya s obostreniem dlya nelineinoi diffuzionnoi sistemy s istochnikom i nelineinymi granichnymi usloviyami”, Vestnik KRAUNTs. Fiz.-mat. nauki, 43:2 (2023), 9–19
Zafar Rakhmonov, Roman Parovik, Akram Alimov, INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020, 2365, INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020, 2021, 060022
M. Aripov, Sh. Sadullaeva, N. Iskhakova, 2020 4th International Symposium on Multidisciplinary Studies and Innovative Technologies (ISMSIT), 2020, 1
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
Z. R. Rakhmonov, J. E. Urunbayev, “on a Problem of Cross-Diffusion With Nonlocal Boundary Conditions”, J. Sib. Fed. Univ.-Math. Phys., 12:5 (2019), 614–620
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
Aripov Mersaid, Springer Proceedings in Mathematics & Statistics, 268, Differential Equations and Dynamical Systems, 2018, 9
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