Global existence of unique strong solutions is proved for the generalized complex Ginzburg-Landau equation. The proof is based on a new type perturbation theorem for -accretive operators in complex Hilbert spaces.
Noboru OKAZAWA. Tomomi YOKOTA. "Perturbation theory for -accretive operators and generalized complex Ginzburg-Landau equations." J. Math. Soc. Japan 54 (1) 1 - 19, January, 2002. https://doi.org/10.2969/jmsj/1191593952