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Construction of blowup solutions for the Complex Ginzburg-Landau equation with critical parameters / Giao Ky Duong, Nejla Nouaili, Hatem Zaag.
Author
Duong, Giao Ky, 1991-
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Format
Book
Language
English
Published/Created
Providence, RI : American Mathematical Society, 2023.
©2023
Description
v, 91 pages ; 26 cm
Details
Subject(s)
Differential equations, Partial
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Mathematical analysis
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Related name
Nouaili, Nejla, 1980-
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Author
Zaag, Hatem
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Series
Memoirs of the American Mathematical Society ; no. 1411.
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Memoirs of the American Mathematical Society ; number 1411
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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.
Bibliographic references
Includes bibliographical references (pages 89-91).
Contents
Chapter 1. Introduction
Chapter 2. Formal approach
Chapter 3. Formulation of the problem
Chapter 4. Existence
Chapter 5. Single point blow-up and final profile.
Show 2 more Contents items
ISBN
1470461218 ((pbk.))
9781470461218 ((pbk.))
OCLC
1381795983
Statement on language in description
Princeton University Library aims to describe library materials in a manner that is respectful to the individuals and communities who create, use, and are represented in the collections we manage.
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Construction of Blowup Solutions for the Complex Ginzburg-Landau Equation with Critical Parameters / Giao Ky Duong, Nejla Nouaili, and Hatem Zaag.
id
99129076620306421