A Liouville theorem for vector valued semilinear heat equations with
no gradient structure and applications to blow-up

Nejla Nouaili
(Département de mathématiques et applications DMA, Ecole Normale Supérieure)

We prove a Liouville Theorem for a vector valued semilinear heat equation with no gradient structure. Classical tools such as the maximum principle or energy techniques break down and have to be replaced by a new approach. We then derive from this theorem uniform estimates for blow-up solutions of that equation.
 

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