In this paper we study blow-up phenomena of the solutions of a reaction-diffusion equation for which the diffusion term corresponds to the diffusion equation in transparent media. We show that for this equation the critical Fujita exponent is smaller than the classical one.
"Critical Fujita exponent for the diffusion equation in transparent media with source having power-like non-linearities." Adv. Differential Equations 18 (3/4) 243 - 264, March/April 2013.