Global existence and nonexistence for a multidimensional system of parabolic equations with nonlinear boundary conditions

In this paper, we study the conditions of global solvability and unsolvability in time of solutions to the nonlinear diffusion problem based on self-similar analysis. We constructed various self-similar solutions of the nonlinear diffusion problem in the slow diffusion case. We established critical exponents of the Fujita type and critical exponents for the global existence of the solution. Using the asymptotic formulas as the initial approximation for the iterative process, numerical calculations are performed.