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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2013, Volume 283, Pages 171–187
DOI: https://doi.org/10.1134/S0371968513040122 (Mi tm3499) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Gradient blow-up of solutions to the Cauchy problem for the Schrödinger equation

V. Zh. Sakbaev

Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region, Russia
Full-text PDF (283 kB) Citations (8)
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DOI: https://doi.org/10.1134/S0371968513040122
Abstract: A class of nonlinear Schrödinger operators with singular coefficients is studied. For this class, necessary and sufficient conditions are established for the existence of initial data such that the corresponding solution to the Cauchy problem blows up in finite time. A regularization procedure for the Cauchy problem is proposed, and the limit behavior of the sequence of solutions to the regularized problems is analyzed.
Received in January 2013
English version:
Proceedings of the Steklov Institute of Mathematics, 2013, Volume 283, Pages 165–180
DOI: https://doi.org/10.1134/S0081543813080129
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
Citation: V. Zh. Sakbaev, “Gradient blow-up of solutions to the Cauchy problem for the Schrödinger equation”, Function theory and equations of mathematical physics, Collected papers. In commemoration of the 90th anniversary of Lev Dmitrievich Kudryavtsev's birth, Trudy Mat. Inst. Steklova, 283, MAIK Nauka/Interperiodica, Moscow, 2013, 171–187; Proc. Steklov Inst. Math., 283 (2013), 165–180
Citation in format AMSBIB
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\paper Gradient blow-up of solutions to the Cauchy problem for the Schr\"odinger equation
\inbook Function theory and equations of mathematical physics
\bookinfo Collected papers. In commemoration of the 90th anniversary of Lev Dmitrievich Kudryavtsev's birth
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\vol 283
\pages 171--187
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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