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Subdifferential operator approach to strong wellposedness of the complex Ginzburg-Landau equation. (English) Zbl 1198.47089
This paper deals with the strong well-posedness of a class of evolutionary initial-boundary value problems for the complex Ginzburg-Landau equation. The main results of the present paper concern the following items: (i) the strong $$L^2$$-wellposedness for $$L^2$$-initial data and (ii) related results for $$H^1_ 0$$-initial data. The proofs rely on techniques about non-contraction semigroups combined with related estimates for semilinear evolution equations.

##### MSC:
 47N20 Applications of operator theory to differential and integral equations 35Q55 NLS equations (nonlinear Schrödinger equations) 47H06 Nonlinear accretive operators, dissipative operators, etc. 47H20 Semigroups of nonlinear operators 47J35 Nonlinear evolution equations
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