Blow-up results for vector-valued nonlinear heat equations with no gradient structure

Hatem Zaag

doi:10.1016/s0294-1449(98)80002-4

JournalsaihpcVol. 15, No. 5pp. 581–622

Blow-up results for vector-valued nonlinear heat equations with no gradient structure

Hatem Zaag
Université de Cergy-Pontoise, École Normale Supérieure, 45, rue d’Ulm, 75005 Paris, France

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Abstract

We construct a blow-up solution for the following nonlinear complex equation:

u_{t} = Δ u + (1 + i δ) ∣ u ∣^{p - 1} u, u \in C .

We also find the asymptotic profile near the singularity, and generalize the result to other vector-valued equations.

Résumé

On construit une solution explosive de l’équation non linéaire complexe suivante:

u_{t} = Δ u + (1 + i δ) ∣ u ∣^{p - 1} u, u \in C .

On donne aussi son profil asymptotique au voisinage de la singularité, et on généralise le résultat à d’autres équations à valeurs vectorielles.

Cite this article

Hatem Zaag, Blow-up results for vector-valued nonlinear heat equations with no gradient structure. Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998), no. 5, pp. 581–622

DOI 10.1016/S0294-1449(98)80002-4