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

Format:

Book

Author/Creator:

Duong, Giao Ky, 1991- author.

Nouaili, Nejla, 1980- author.

Zaag, Hatem, author.

Series:

Memoirs of the American Mathematical Society ; Volume 285.

Memoirs of the American Mathematical Society Series ; Volume 285

Language:

English

Subjects (All):

Blowing up (Algebraic geometry).

Reaction-diffusion equations.

Physical Description:

1 online resource (104 pages)

Edition:

First edition.

Place of Publication:

Providence, RI : American Mathematical Society, [2023]

Summary:

"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.

Contents:

Formal approach

Formulation of the problem

Existence

Single point blow-up and final profile.

Notes:

Description based on print version record.

Includes bibliographical references.

Other Format:

Print version: Duong, Giao Ky Construction of Blowup Solutions for the Complex Ginzburg-Landau Equation with Critical Parameters

ISBN:

9781470474812

1470474816