Blow up profiles for a quasilinear reaction-diffusion equation with weighted reaction

We perform a thorough study of the blow up profiles associated to following second order reaction-diffusion equation with non-homogeneous reaction:?tu=?xx(um)+|x|?up, in range exponents 10. classify solutions self-similar form, that are likely represent typical patterns for general solutions. thus show coefficient |x|? has strong influence on qualitative aspects related finite time up. More precisely, ??0, have similar behavior well-established homogeneous case ?=0, typically global occurs, while ?>0 sufficiently large, there exist which occurs only at space infinity, contrast case. This work is part larger program understanding unbounded weights equations.