“…While a detailed analysis of selfsimilarity for the case σ = 0 is available in [32,Chapter 4], previous works on different ranges of the exponents m, p and σ > 0 led to some completely novel and, in many occasions, unexpected forms and behaviors of the profiles, see for example [15] (for p = 1 and σ > 0), [18] (for p ∈ (1, m) and σ > 0) or [16,20] (for p = m and dimensions N = 1, respectively N ≥ 2), all them for the range m > 1. A separate mention has to be given to the works [17,19], dealing with our range of exponents (1.2) but for dimension N = 1, where we classify the self-similar blow-up profiles and obtain that there are two different types of compactly supported profiles, depending on the interface behavior and also on the sign of the number m + p − 2, a fact that is in line with the more qualitative study performed in the series of papers by De Pablo and Vázquez [26,27,28] for the homogeneous equation, that is, Eq. (1.1) with σ = 0.…”