Critical exponents for a fast diffusive polytropic filtration equation with nonlinear boundary flux

In this paper, we deal with a fast diffusive polytropic filtration equation ∂u ∂t = ∂ ∂x ∂um ∂x p−2 ∂um ∂x 1 < p < 1+ 1 m in R+ × (0,+∞), subject to a nonlinear boundary flux −|∂um ∂x |p−2 ∂um ∂x (0, t) = uq(0, t), t ∈ (0,+∞). We first get the behavior of the solution at infinity, and establish the critical global existence exponent and critical Fujita exponent for the fast diffusive polytropic filtration equation, furthermore give the blow-up set and upper bound of the blow-up rate for the nonglobal solutions.