Study of the Blow-up Set by Transformation

We obtain some new results on blow-up for the heat equation with nonlinear sources by transformation into an absorption problem. Our work is related to that of Kawohl and Peletier who first developed such a transformation in some special cases. Here we provide a systematic method for constructing a suitable transformation by using the class of regularly varying functions. Through regularization we obtain a precise characterization of the blow-up set as zeros of a certain e-steadystate