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Volume 16, Issue 4
The Self-similar Solution for Ginzburg-Landau Equation and Its Limit Behavior in Besov Spaces

Xiaoyi Zhang

J. Part. Diff. Eq., 16 (2003), pp. 361-375.

Published online: 2003-11

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  • Abstract
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.
  • Keywords

Ginzburg-Landau equation Schrödinger equation self-similar solution limit behavior

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@Article{JPDE-16-361, author = {Xiaoyi Zhang }, title = {The Self-similar Solution for Ginzburg-Landau Equation and Its Limit Behavior in Besov Spaces}, journal = {Journal of Partial Differential Equations}, year = {2003}, volume = {16}, number = {4}, pages = {361--375}, abstract = { 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.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5432.html} }
TY - JOUR T1 - The Self-similar Solution for Ginzburg-Landau Equation and Its Limit Behavior in Besov Spaces AU - Xiaoyi Zhang 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.
Xiaoyi Zhang . (2003). The Self-similar Solution for Ginzburg-Landau Equation and Its Limit Behavior in Besov Spaces. Journal of Partial Differential Equations. 16 (4). 361-375. doi:
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