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Izvestiya: Mathematics, 2011, Volume 75, Issue 5, Pages 871–887
DOI: https://doi.org/10.1070/IM2011v075n05ABEH002556 (Mi im4079) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On the Cauchy problem for a Sobolev-type equation with quadratic non-linearity

A. I. Aristov
English version PDF (271 kB) Citations (2)
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DOI: https://doi.org/10.1070/IM2011v075n05ABEH002556
Abstract: We investigate the asymptotic behaviour as $t\to\infty$ of the solution of the Cauchy problem for a Sobolev-type equation with quadratic non-linearity and develop ideas used by I. A. Shishmarev and other authors in the study of classical and Sobolev-type equations. Conditions are found under which it is possible to consider the case of an arbitrary dimension of the spatial variable.
Keywords: non-linear partial differential equations, Sobolev-type equations, asymptotic behaviour of solutions, perturbation theory.
Received: 26.01.2009
Revised: 05.05.2010
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2011, Volume 75, Issue 5, Pages 3–18
DOI: https://doi.org/10.4213/im4079
Bibliographic databases:
Document Type: Article
UDC: 517.955.8
MSC: Primary 35C20; Secondary 35K60, 76B15
Language: English
Original paper language: Russian
Citation: A. I. Aristov, “On the Cauchy problem for a Sobolev-type equation with quadratic non-linearity”, Izv. RAN. Ser. Mat., 75:5 (2011), 3–18; Izv. Math., 75:5 (2011), 871–887
Citation in format AMSBIB
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  • https://doi.org/10.1070/IM2011v075n05ABEH002556
  • https://www.mathnet.ru/eng/im/v75/i5/p3
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Russian version PDF:189
    English version PDF:15
    References:99
    First page:35
     
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