Critical exponents for the multidimensional polytrophic filtration problem with a variable coefficients and nonlocal boundary condition

In this paper we study the global solvability and no solvability conditions of a multidimensional nonlinear problem of non-Newtonian filtration with nonlocal boundary condition in the slow diffusion case. Establish the critical global existence exponent and critical Fujita exponent of nonlinear filtration problem in inhomogeneous medium, which play an important role in the study of qualitative properties of nonlinear models of reaction - diffusion, thermal conductivity, filtering, and other physical, chemical, and biological processes. In the global solvability case the main terms of the asymptotic of solutions is obtained.

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