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Izvestiya: Mathematics, 2015, Volume 79, Issue 5, Pages 955–1012
DOI: https://doi.org/10.1070/IM2015v079n05ABEH002768 (Mi im8285) 		 
This article is cited in 34 scientific papers (total in 34 papers)

Critical exponents of instantaneous blow-up or local solubility of non-linear equations of Sobolev type

M. O. Korpusov

M. V. Lomonosov Moscow State University, Faculty of Physics
English version PDF (603 kB) Citations (34)
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DOI: https://doi.org/10.1070/IM2015v079n05ABEH002768
Abstract: We consider Cauchy problems for a class of non-linear equations of Sobolev type. It is shown that for such problems there is a critical exponent (depending on the dimension of the space $\mathbb{R}^N$) according to which a weak local solution either exists uniquely or does not exist.
Keywords: Fujita's critical exponent, non-linear equations of Sobolev type, blow-up, local solubility, non-linear capacity.
Received: 14.08.2014
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2015, Volume 79, Issue 5, Pages 103–162
DOI: https://doi.org/10.4213/im8285
Bibliographic databases:
Document Type: Article
UDC: 517.538
MSC: 35B44, 35A01, 35G31
Language: English
Original paper language: Russian
Citation: M. O. Korpusov, “Critical exponents of instantaneous blow-up or local solubility of non-linear equations of Sobolev type”, Izv. Math., 79:5 (2015), 955–1012
Citation in format AMSBIB
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\by M.~O.~Korpusov
\paper Critical exponents of instantaneous blow-up or local solubility of non-linear equations of Sobolev type
\jour Izv. Math.
\yr 2015
\vol 79
\issue 5
\pages 955--1012
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  • https://doi.org/10.1070/IM2015v079n05ABEH002768
  • https://www.mathnet.ru/eng/im/v79/i5/p103
    • This publication is cited in the following 34 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Russian version PDF:272
    English version PDF:40
    References:88
    First page:62
     
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