Construction of Blowup Solutions for the Complex Ginzburg-Landau Equation with Critical Parameters / Giao Ky Duong, Nejla Nouaili, and Hatem Zaag.

Author
Duong, Giao Ky, 1991- [Browse]
Format
Book
Language
English
Εdition
First edition.
Published/​Created
  • Providence, RI : American Mathematical Society, [2023]
  • ©2023
Description
1 online resource (104 pages)

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Series
Summary note
"We construct a solution for the Complex Ginzburg-Landau (CGL) equation in a general critical case, which blows up in finite time T only at one blow-up point. We also give a sharp description of its profile. In the first part, we formally construct a blow-up solution. In the second part we give the rigorous proof. 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. We would like to mention that the asymptotic profile of our solution is different from previously known profiles for CGL or for the semilinear heat equation"-- Provided by publisher.
Bibliographic references
Includes bibliographical references.
Source of description
Description based on print version record.
Contents
  • Formal approach
  • Formulation of the problem
  • Existence
  • Single point blow-up and final profile.
ISBN
1-4704-7481-6
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