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Mat. Zametki, 2019, Volume 105, Issue 1, Pages 76–83 (Mi mz11559)  

On the Collapse of Solutions of the Cauchy Problem for the Cubic Schrödinger Evolution Equation

Sh. M. Nasibov

Institute of Applied Mathematics, Baku State University

Abstract: It is proved that, for some initial data, the solutions of the Cauchy problem for the cubic Schrödinger evolution equation blow up in finite time whose exact value is estimated from above. In addition, lower bounds for the blow-up rate of the solution in certain norms are obtained.

Keywords: Schrödinger equation, Cauchy problem, interpolation inequality.

DOI: https://doi.org/10.4213/mzm11559

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English version:
Mathematical Notes, 2019, 105:1, 64–70

Bibliographic databases:

Document Type: Article
UDC: 517.946
Received: 18.02.2017
Revised: 14.11.2017

Citation: Sh. M. Nasibov, “On the Collapse of Solutions of the Cauchy Problem for the Cubic Schrödinger Evolution Equation”, Mat. Zametki, 105:1 (2019), 76–83; Math. Notes, 105:1 (2019), 64–70

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