scholarly journals Asymptotic behavior of solutions of complex discrete evolution equations: The discrete Ginzburg-Landau equation

2007 ◽  
Vol 19 (4) ◽  
pp. 711-736 ◽  
Author(s):  
N. I. Karachalios ◽  
◽  
Hector E. Nistazakis ◽  
Athanasios N. Yannacopoulos ◽  
◽  
...  
Keyword(s):  
Asymptotic Behavior ◽  
Evolution Equations ◽  
Landau Equation ◽  
Asymptotic Behavior Of Solutions ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Discrete Evolution Equations

scholarly journals Asymptotic behavior of random coupled Ginzburg–Landau equation driven by colored noise on unbounded domains

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zhang Chen ◽  
Lingyu Li ◽  
Dandan Yang
Keyword(s):  
Asymptotic Behavior ◽  
Lipschitz Condition ◽  
Colored Noise ◽  
Nonlinear Term ◽  
Coupling Parameter ◽  
Landau Equation ◽  
Unbounded Domains ◽  
Ginzburg Landau ◽  
Local Lipschitz Condition ◽  
Ginzburg Landau Equation

AbstractIn this paper, a random coupled Ginzburg–Landau equation driven by colored noise on unbounded domains is considered, in which the nonlinear term satisfies a local Lipschitz condition. It is shown that the random attractor of such a coupled Ginzburg–Landau equation is a singleton set, and the components of solutions are very close when the coupling parameter becomes large enough.

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