Profile for a Simultaneously Blowing up Solution to a Complex Valued Semilinear Heat Equation

Nouaili, Nejla; Zaag, Hatem

Nouaili, Nejla; Zaag, Hatem (2015), Profile for a Simultaneously Blowing up Solution to a Complex Valued Semilinear Heat Equation, Communications in Partial Differential Equations, 40, 7, p. 1197-1217. 10.1080/03605302.2015.1018997

Type

Article accepté pour publication ou publié

Lien vers un document non conservé dans cette base

https://arxiv.org/abs/1306.4435v4

Date

2015

Nom de la revue

Communications in Partial Differential Equations

Volume

Numéro

Éditeur

Marcel Dekker

Ville d’édition

Paris

Pages

1197-1217

Résumé (EN)

We construct a solution to a complex nonlinear heat equation which blows up in finite time T only at one blow-up point. We also give a sharp description of its blow-up profile. The proof relies on the reduction of the problem to a finite dimensional one and the use of index theory to conclude. We note that the real and imaginary parts of the constructed solution blow up simultaneously, with the imaginary part dominated by the real.

Mots-clés

Simultaneous blow-up; Complex heat equation