抄録
This paper is concerned with the Cauchy problem for a fast diffusion equation involving a variable exponent ut = Δum + 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 = Δum + 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.