Construction of a blow-up solution for the Complex Ginzburg-Landau equation in some critical case

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 theor...

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Veröffentlicht in:Archive for rational mechanics and analysis 2018, Vol.228 (3)
Hauptverfasser: Nouaili, Nejla, Zaag, Hatem
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0003-9527
1432-0673