Construction of a blow-up solution for a complex nonlinear heat equation.

Nejla Nouaili (1) , Hatem Zaag (2)

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

We construct a solution to a complex nonlinear heat equation which blows up in nite time T only at one blow-up point. We also give a sharp description of its blow-up pro le. The proof relies on the reduction of the problem to a nite 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.

Mots clés: Complex heat equation; Simultaneous blow-up; Complex heat equation.

Domaines: Equations aux dérivées partielles [math.AP]

Nejla Nouaili, Hatem Zaag. Construction of a blow-up solution for a complex nonlinear heat equation.. 2013. ⟨hal-00835338⟩