This paper is concerned with the Cauchy problem for a fast diffusion equation involving a variable exponent
ut = Δ
um +
up(x) in
Rn, where
m is a constant such that max{0, 1 − 2/
n} <
m < 1 and
p(
x) is a continuous bounded function such that 1 <
p− = inf
p ≤
p(
x) ≤ sup
p =
p+. Since the thermal conductively
mum−1 ↑ ∞ when
u ↓ 0, mathematically
ut = Δ
um +
up(x) represents a fast diffusion with source. The initial condition
u0(
x) is assumed to be continuous, nonnegative and bounded. For the non-decaying initial data at space infinity, any nontrivial nonnegative solutions blow up in finite time. We give the upper bound of the blow-up time of positive solutions of a fast diffusion equation for the non-decaying initial data at space infinity.
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