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The Cauchy problem in local spaces for the complex Ginzburg-Landau equation. II: Contraction methods. (English) Zbl 0889.35046
The present paper is a continuation of the previous work of the same authors [Physica D, 191-228 (1995; reviewed above)]. Treating the same problems by means of contraction methods, the authors prove the uniqueness of solutions under some subcriticality conditions, and obtain additional regularity properties and uniform bounds.

MSC:
35K55 Nonlinear parabolic equations
35K15 Initial value problems for second-order parabolic equations
35Q55 NLS equations (nonlinear Schrödinger equations)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B65 Smoothness and regularity of solutions to PDEs
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