Similarity stabilizes blow-up
Journées équations aux dérivées partielles (1999), article no. 12, 7 p.

The blow-up of solutions to a quasilinear heat equation is studied using a similarity transformation that turns the equation into a nonlocal equation whose steady solutions are stable. This allows energy methods to be used, instead of the comparison principles used previously. Among the questions discussed are the time and location of blow-up of perturbations of the steady blow-up profile.

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Steve Schochet. Similarity stabilizes blow-up. Journées équations aux dérivées partielles (1999), article  no. 12, 7 p. https://proceedings.centre-mersenne.org/item/JEDP_1999____A12_0/

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[S] S. Schochet : Similarity stabilizes blow-up in quasilinear parabolic equations with balanced nonlinearity, in preparation.