Continuity of the blow-up profile with respect to initial data and to the blow-up point for a semilinear heat equation

Saima Khenissy (1) , Yomna Rébaï (2) , Hatem Zaag (3)

1 ISI - Département de Mathématiques Appliquées
2 FSB - Département de mathématiques
3 LAGA - Laboratoire Analyse, Géométrie et Applications

We consider blow-up solutions for semilinear heat equations with Sobolev subcritical power nonlinearity. Given a blow-up point $\hat{a}$, we have from earlier literature, the asymptotic behavior in similarity variables. Our aim is to discuss the stability of that behavior, with respect to perturbations in the blow-up point and in initial data. Introducing the notion of ``profile order", we show that it is upper semicontinuous, and continuous only at points where it is a local minimum.

Domaines: Equations aux dérivées partielles [math.AP]

Saima Khenissy, Yomna Rébaï, Hatem Zaag. Continuity of the blow-up profile with respect to initial data and to the blow-up point for a semilinear heat equation. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2011, 28 (1), pp.1-26. ⟨10.1016/j.anihpc.2010.09.006⟩. ⟨hal-00570173⟩