|  Abstract:  | 
         
        
          | In this talk, we consider the non-homogeneous boundary value problem for the complex Ginzburg-Landau equation with Dirichlet or Neumann boundary conditions.  Both local and global well-posedness in the Sobolev space with negative indices are discussed. Moreover, a comparision of our results with those for the corresponding Cauchy problem is made. | 
         
     
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