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Monotonicity method applied to the complex Ginzburg-Landau and related equations. (English) Zbl 0995.35029
A new inequality in monotonicity methods is derived. It is based on the sectorial estimates of $$-\Delta$$ in $$L^{p+1}$$ and the nonlinear operator $$u\mapsto|u|^{p-1}u$$ appearing in the equation.
By the inequality the global existence of unique strong solutions is established for the complex Ginzburg-Landau equation. The inequality also yields the global existence of unique strong solution for nonlinear Schrödinger type equation with monotone nonlinearity.
Reviewer: X.Xiang (Guiyang)

##### MSC:
 35K55 Nonlinear parabolic equations 35Q55 NLS equations (nonlinear Schrödinger equations) 35B45 A priori estimates in context of PDEs
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##### References:
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