This article is cited in 3 scientific papers (total in 3 papers)
On the properties of solutions of multidimensional nonlinear filtration problem with variable density and nonlocal boundary condition in the case of fast diffusion
Zafar R. Rakhmonov
National University of Uzbekistan, 100174, University street, 4, Tashkent, Uzbekistan
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.
filtration, asymptotics, critical exponent, inhomogeneous density.
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Received in revised form: 04.12.2015
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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\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.
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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
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
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