NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2018, 9 (3), P. 323–329
On the behavior of the solution of a nonlinear polytropic filtration problem with a source and multiple nonlinearities
Z. R. Rakhmonov – National University of Uzbekistan, Applied Mathematics and Computer Analysis, Universitet, 4, Tashkent, 100174, Uzbekistan; firstname.lastname@example.org
A. I. Tillaev – National University of Uzbekistan, Applied Mathematics and Computer Analysis, Universitet, 4, Tashkent, 100174, Uzbekistan; email@example.com
In this paper, we study the global solvability and unsolvability conditions of a nonlinear filtration problem with nonlinear boundary flux. We establish the critical global existence exponent and critical Fujita exponent of nonlinear filtration problem in inhomogeneous medium. An asymptotic representation of the solution with a compact support is obtained, which made it possible to carry out a numerical experiment.
Keywords: filtration, global solutions, blow-up, critical curve, asymptotic behavior, numerical analysis.
PACS 02.30.Jr, 02.30.Mv, 02.60.-x, 11.10.Jj, 11.10.Lm