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.


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