## 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.

Original language | English (US) |
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Pages (from-to) | 1613-1666 |

Number of pages | 54 |

Journal | Journal of Functional Analysis |

Volume | 255 |

Issue number | 7 |

DOIs | |

State | Published - Oct 1 2008 |

## Keywords

- Blow-up profile
- Blow-up solution
- Complex Ginzburg-Landau equation
- Stability

## ASJC Scopus subject areas

- Analysis