A simplified proof of a Liouville theorem for nonnegative solution of a subcritical semilinear heat equations

Nejla Nouaili (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

We give a new proof of the Liouville theorem proved by Merle and Zaag for nonnegative solutions of the semilinear heat equation with power nonlinearity. Our proof has a pedagogical interest and is based on Kaplan's blow-up criterion.

Mots clés: Heat equation; Liouville theorem; Blow-up; Kaplan's criterion

Domaines: Equations aux dérivées partielles [math.AP]

Nejla Nouaili. A simplified proof of a Liouville theorem for nonnegative solution of a subcritical semilinear heat equations. Journal of Dynamics and Differential Equations, 2009, 21 (1), pp.127-132. ⟨10.1007/s10884-008-9121-6⟩. ⟨hal-00701234⟩