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Izv. RAN. Ser. Mat., 2011, Volume 75, Issue 5, Pages 3–18 (Mi izv4079)  

This article is cited in 1 scientific paper (total in 1 paper)

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

A. I. Aristov


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.

DOI: https://doi.org/10.4213/im4079

Full text: PDF file (460 kB)
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English version:
Izvestiya: Mathematics, 2011, 75:5, 871–887

Bibliographic databases:

UDC: 517.955.8
MSC: Primary 35C20; Secondary 35K60, 76B15
Received: 26.01.2009
Revised: 05.05.2010

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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  • http://mi.mathnet.ru/eng/izv4079
  • https://doi.org/10.4213/im4079
  • http://mi.mathnet.ru/eng/izv/v75/i5/p3

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. I. Aristov, “On the Cauchy problem for a nonlinear Sobolev type equation”, Differ. Equ., 50:1 (2014), 117–121  crossref  crossref  mathscinet  zmath  isi  elib  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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