KIT - Department of Mathematics - Blow-up for the Complex Ginzburg-Landau in some critical case

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PDE-Seminar: Talk by Hatem Zaag

PDE-Seminar: Talk by Hatem Zaag

Blow-up for the Complex Ginzburg-Landau in some critical case

Speaker: Dr. Hatem Zaag
Place: Seminar room 1.067, Building 20.30
Time: 25.10.2018, 14:00 - 15:00
Invited by: CRC 1173

Abstract

We construct a solution for the Complex Ginzburg-Landau equation in some critical case, which blows up in finite time $T$ only at one blow-up point. We also give a sharp description of its profile. The proof relies on the reduction of the problem to a finite dimensional one, and the use of index theory to conclude. The interpretation of the parameters of the finite dimension problem in terms of the blow-up point and time allows to prove the stability of the constructed solution. This is a joint work with Nejla Nouaili from Université Paris Dauphine.