Construction of a Blow-Up Solution for the Complex Ginzburg-Landau Equation in a Critical Case

被引：17

作者：

Nouaili, Nejla ^{[1
]}

Zaag, Hatem ^{[2
]}

机构：

[1] PSL Res Univ, Univ Paris auphine 09, CEREMADE, UMR 7534, F-75016 Paris, France

[2] Univ Paris 13, Sorbonne Paris Cite, LAGA, CNRS,UMR 7539, F-93430 Villetaneuse, France

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2018年 / 228卷 / 03期

关键词：

SEMILINEAR HEAT-EQUATIONS; NO GRADIENT STRUCTURE; LIOUVILLE THEOREM; MULTI-BUMP; FLOW; CONVECTION; STABILITY; BEHAVIOR; SET;

D O I：

10.1007/s00205-017-1211-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：995 / 1058

页数：64

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