
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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Article accepté pour publication ou publiéDate
2018Journal name
Archive for Rational Mechanics and AnalysisVolume
228Number
3Publisher
Springer
Pages
995-1058
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Show full item recordAbstract (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 profileRelated items
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