In this paper we consider the evolution of positive bounded uniformly continuous data u0 by perturbed equations like
Under general assumptions on u0, existence, uniqueness and regularity of the evolution u in the set
are studied, where the blow-up function is given by .
The exact blow-up rate of u is obtained. Uniqueness, regularity, decay at infinity of the function , as well a s a representation formula for the case m = 1, are also proved.