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Funktsional'nyi Analiz i ego Prilozheniya, 2012, Volume 46, Issue 4, Pages 51–60
DOI: https://doi.org/10.4213/faa3087 (Mi faa3087) 		 
This article is cited in 10 scientific papers (total in 10 papers)

On the Nonexistence of Global Solutions of the Cauchy Problem for the Korteweg–de Vries Equation

S. I. Pokhozhaev

Steklov Mathematical Institute of the Russian Academy of Sciences
Full-text PDF (150 kB) Citations (10)
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DOI: https://doi.org/10.4213/faa3087
Abstract: We establish conditions on the initial data under which the Cauchy problem for the Korteweg–de Vries equation does not admit a solution global in $t>0$. The proof of the results is based on the nonlinear capacity method (Dokl. RAN, 357:5 (1997), 592–594). In closing, we provide an example.
Keywords: blow-up, KdV equation, initial-boundary value problem, Cauchy problem, nonlinear capacity.
Funding agency Grant number
Russian Foundation for Basic Research 11-01-00348_а
11-01-12018_офи_м
Received: 07.09.2011
English version:
Functional Analysis and Its Applications, 2012, Volume 46, Issue 4, Pages 279–286
DOI: https://doi.org/10.1007/s10688-012-0035-z
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: S. I. Pokhozhaev, “On the Nonexistence of Global Solutions of the Cauchy Problem for the Korteweg–de Vries Equation”, Funktsional. Anal. i Prilozhen., 46:4 (2012), 51–60; Funct. Anal. Appl., 46:4 (2012), 279–286
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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