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

Nejla Nouaili (1) , Hatem Zaag (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LAGA - Laboratoire Analyse, Géométrie et Applications

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.

Mots clés: Vector-valued; Blow-up; Liouville theorem; Uniform estimates; Heat equation; Vector-valued.

Domaines: Equations aux dérivées partielles [math.AP]

Nejla Nouaili, Hatem Zaag. A Liouville theorem for vector valued semilinear heat equations with no gradient structure and applications to blow-up. Transactions of the American Mathematical Society, 2010, 362 (7), pp.3391-3434. ⟨hal-00531306⟩