Properties of solutions of a system of nonlinear parabolic equations with nonlinear boundary conditions.

In this paper, we study the global solvability and unsolvability of one nonlinear system of non-Newtonian polytropic filtration with a nonlocal boundary condition in the case of slow diffusion. We are constructed various self-similar solutions to the nonlinear filtration problem in the slow diffusion case. The conditions for the global existence of a solution in time and unsolvability of the solution of the nonlinear filtration problem based on the method of standard equations, self-similar analysis and comparison principles are found. Establish the critical global existence exponent and critical Fujita exponent, which play an important role in the study of qualitative properties of nonlinear models of nonlinear reaction-diffusion, thermal conductivity, filtration, and other physical, chemical, and biological processes. In the case of the global solvability the main term of the asymptotics of solutions obtain. For the numerical investigation of the nonlinear filtration problem is provided a method of selecting suitable initial approximation for the iterative process. Using asymptotic formulas as the initial approximation for the iterative process, numerical calculations and analysis of the results are performed. [ABSTRACT FROM AUTHOR]