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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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