Abstract :
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.
