FINITE-TIME BLOWUP FOR A COMPLEX GINZBURG-LANDAU EQUATION

被引：36

作者：

Cazenave, Thierry ^{[1
,2
]}

Dickstein, Flavio ^{[3
]}

Weissler, Fred B. ^{[4
]}

机构：

[1] Univ Paris 06, F-75252 Paris 05, France

[2] CNRS, Lab Jacques Louis Lions, F-75252 Paris 05, France

[3] Univ Fed Rio de Janeiro, Inst Matemat, BR-21944970 Rio De Janeiro, RJ, Brazil

[4] Univ Paris 13, CNRS UMR LAGA 7539, F-93430 Villetaneuse, France

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2013年 / 45卷 / 01期

关键词：

complex Ginzburg-Landau equation; finite-time blowup; energy; variance; CAUCHY-PROBLEM; PARABOLIC EQUATIONS; MONOTONICITY METHOD; LOCAL SPACES; BLOWING-UP; NONEXISTENCE; EXISTENCE; THEOREMS;

D O I：

10.1137/120878690

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that negative energy solutions of the complex Ginzburg-Landau equation e-(i theta)u(t) = Delta u + vertical bar u vertical bar(alpha)u blow up in finite time, where alpha > 0 and -pi/2 < theta < pi/2. For a fixed initial value u(0), we obtain estimates of the blow-up time T-max(theta) as theta -> +/-pi/2. It turns out that T-max(theta) stays bounded (respectively, goes to infinity) as theta -> +/-pi/2 in the case where the solution of the limiting nonlinear Schrodinger equation blows up in finite time (respectively, is global).

引用

页码：244 / 266

页数：23

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