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