TY - JOUR
T1 - The Self-similar Solution for Ginzburg-Landau Equation and Its Limit Behavior in Besov Spaces
JO - Journal of Partial Differential Equations
VL - 4
SP - 361
EP - 375
PY - 2003
DA - 2003/11
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5432.html
KW - Ginzburg-Landau equation
KW - Schrödinger equation
KW - self-similar solution
KW - limit behavior
AB -  In this paper, we study the limit behavior of self-similar solutions for the Complex Ginzburg-Landau (CGL) equation in the nonstandard function space E_{s,p}. We prove the uniform existence of the solutions for the CGL equation and its limit equation in E_{s,p}. Moreover we show that the self-similar solutions of CGL equation converge, globally in time, to those of its limit equation as the parameters tend to zero. Key Words Ginzburg-Landau equation; Schrödinger equation; self-similar solution; limit behavior.