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Perturbation theory for $$m$$-accretive operators and generalized complex Ginzburg-Landau equations. (English) Zbl 1045.35080
The authors establish the existence and uniqueness of global strong solutions for an initial-boundary value problem associated with the generalized Ginzburg-Landau equation. The approach is based on a new $$m$$-accretivity result for the linear combination of a linear nonnegative self-adjoint operator, and a nonlinear $$m$$-accretive operator in a complex Hilbert space.

##### MSC:
 35Q55 NLS equations (nonlinear Schrödinger equations) 47H06 Nonlinear accretive operators, dissipative operators, etc. 35B25 Singular perturbations in context of PDEs
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