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• W2048316986 abstract "We construct a solution to the complex Ginzburg–Landau equation, which blows up in finite time T only at one blow-up point. We also give a sharp description of its blow-up profile. The proof relies on the reduction of the problem to a finite-dimensional one, and the use of index theory to conclude. Two major difficulties arise in the proof: the linearized operator around the profile is not self-adjoint and it has a second neutral mode. In the last section, the interpretation of the parameters of the finite-dimensional problem in terms of the blow-up time and the blow-up point gives the stability of the constructed solution with respect to perturbations in the initial data." @default.
• W2048316986 created "2016-06-24" @default.
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• W2048316986 date "2008-10-01" @default.
• W2048316986 modified "2023-09-30" @default.
• W2048316986 title "Blow-up profile for the complex Ginzburg–Landau equation" @default.
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• W2048316986 doi "https://doi.org/10.1016/j.jfa.2008.03.008" @default.
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