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On some sufficient conditions for the blow-up solutions of the nonlinear Ginzburg-Landau-Schrödinger evolution equation. (English) Zbl 1084.35095

Summary: Investigation of the blow-up in finite time of the first mixed boundary-value problem with homogeneous boundary condition on a bounded domain of \(n\)-dimensional Euclidean space for a class of nonlinear Ginzburg-Landau-Schrödinger evolution equation is continued [cf. Sh. M. Nasibov, Dokl. Math. 63, No. 1, 123–125 (2001); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 376, No. 5, 605–607 (2001; Zbl 1048.35109)]. New simple sufficient conditions are obtained for a wide class of initial data under which collapse happens for the given new values of parameters.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35B40 Asymptotic behavior of solutions to PDEs
82D55 Statistical mechanics of superconductors

Citations:

Zbl 1048.35109
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