Construction of a Blow-Up Solution for the Complex Ginzburg–Landau Equation in a Critical Case
We construct a solution for the Complex Ginzburg–Landau equation in a 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...
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Published in | Archive for rational mechanics and analysis Vol. 228; no. 3; pp. 995 - 1058 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.06.2018
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Subjects | |
Online Access | Get full text |
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Summary: | We construct a solution for the Complex Ginzburg–Landau equation in a 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 us to prove the stability of the constructed solution. |
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ISSN: | 0003-9527 1432-0673 |
DOI: | 10.1007/s00205-017-1211-3 |