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

Nouaili, Nejla; Zaag, Hatem (2018), Construction of a blow-up solution for the Complex Ginzburg-Landau equation in some critical case, Archive for Rational Mechanics and Analysis, 228, 3, p. 995-1058. 10.1007/s00205-017-1211-3

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Type
Article accepté pour publication ou publié
Date
2018
Journal name
Archive for Rational Mechanics and Analysis
Volume
228
Number
3
Publisher
Springer
Pages
995-1058
Publication identifier
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Author(s)
Nouaili, Nejla

Zaag, Hatem cc
Abstract (EN)
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.
Subjects / Keywords
Complex Ginzburg-Landau equation; Blow-up profile