A GENERALIZED COMPLEX GINZBURG-LANDAU EQUATION: GLOBAL EXISTENCE AND STABILITY RESULTS

被引：1
|
作者：
Correia, Simao [1 ]
Figueira, Mario [2 ]
机构：
[1] Univ Lisbon, Inst Super Tecn, Dept Math, Ctr Math Anal Geometry & Dynam Syst, Av Rovisco Pais, P-1049001 Lisbon, Portugal
[2] Univ Lisbon, CMAF CIO, Edificio C6, P-1749016 Lisbon, Portugal
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2021年 / 20卷 / 05期
关键词：
complex Ginzburg-Landau; stability; periodic solutions; FINITE-TIME BLOWUP; STANDING WAVES; CAUCHY-PROBLEM; LOCAL SPACES;
D O I：
10.3934/cpaa.2021056
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the complex Ginzburg-Landau equation with two pure-power nonlinearities and a damping term. After proving a general global existence result, we focus on the existence and stability of several periodic orbits, namely the trivial equilibrium, bound-states and solutions independent of the spatial variable. In particular, we construct bound-states either explicitly in the real line or through a bifurcation argument for a double eigenvalue of the Dirichlet-Laplace operator on bounded domains.
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页码：2021 / 2038
页数：18
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