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# Subdifferential operator approach to strong wellposedness of the complex Ginzburg-Landau equation

• Two theorems concerning strong wellposedness are established for the complex Ginzburg-Landau equation. One of them is concerned with strong $L^{2}$-wellposedness, that is, strong wellposedness for $L^{2}$-initial data. The other deals with $H_{0}^{1}$-initial data as a partial extension. By a technical innovation it becomes possible to prove the convergence of approximate solutions without compactness. This type of convergence is known with accretivity methods when the argument of the complex coefficient is small. The new device yields the generation of a class of non-contraction semigroups even when the argument is large. The results are both obtained as application of abstract theory of semilinear evolution equations with subdifferential operators.
Mathematics Subject Classification: Primary: 47H06, 47H20; Secondary: 35Q55.

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