On the properties of solutions of multidimensional nonlinear filtration problem with variable density and nonlocal boundary condition in the case of fast diffusion

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.