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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2011, Issue 1(22), Pages 16–27 (Mi vsgtu938)  

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

Procedings of the 2nd International Conference "Mathematical Physics and its Applications"
Mathematical Physics

On nonlocal cosmological equations on half-line

I. Ya. Aref'eva, I. V. Volovich

Dept. of Mathematical Physics, Steklov Mathematical Institute, Russian Academy of Sciences, Moscow

Abstract: A system of nonlocal cosmological equations where the time variable runs over a half-line is considered. These equations are more suitable for description of the Universe than the previously discussed cosmological equations on the whole line since the Friedmann metric contains a singularity at the beginning of time. Definition of the exponential operator includes a new arbitrary function which is absent in the equations on the whole line. It is shown that this function could be choosen in such a way that one of the slow roll parameters in the chaotic inflation scenario can be made arbitrary small. Solutions of the linearized nonlocal equations on the half-line are constructed.

Keywords: equations with an infinite number of derivatives, cosmological models, heat conduction equation

DOI: https://doi.org/10.14498/vsgtu938

Full text: PDF file (599 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

Document Type: Article
UDC: 517.956.4:524.834
MSC: 83F05
Original article submitted 22/III/2011
revision submitted – 27/III/2011

Citation: I. Ya. Aref'eva, I. V. Volovich, “On nonlocal cosmological equations on half-line”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(22) (2011), 16–27

Citation in format AMSBIB
\Bibitem{AreVol11}
\by I.~Ya.~Aref'eva, I.~V.~Volovich
\paper On nonlocal cosmological equations on half-line
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2011
\vol 1(22)
\pages 16--27
\mathnet{http://mi.mathnet.ru/vsgtu938}
\crossref{https://doi.org/10.14498/vsgtu938}
\elib{http://elibrary.ru/item.asp?id=16387154}


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    This publication is cited in the following articles:
    1. Kh. A. Khachatryan, “Positive solubility of some classes of non-linear integral equations of Hammerstein type on the semi-axis and on the whole line”, Izv. Math., 79:2 (2015), 411–430  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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