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).
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页码：244 / 266
页数：23
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