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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.], 2017, Volume 21, Number 1, Pages 7–41 (Mi vsgtu1529)  

This article is cited in 4 scientific papers (total in 4 papers)

Differential Equations and Mathematical Physics

On a speed of solutions stabilization of the Cauchy problem for the Carleman equation with periodic initial data

S. A. Dukhnovskii

National Research Moscow State University of Civil Engineering, Moscow, 129337, Russian Federation

Abstract: This article explores a one-dimensional system of equations for the discrete model of a gas (Carleman system of equations). The Carleman system is the Boltzmann kinetic equation of a model one-dimensional gas consisting of two particles. For this model, momentum and energy are not retained. On the example of the Carleman model, the essence of the Boltzmann equation can be clearly seen. It describes a mixture of “competing” processes: relaxation and free movement. We prove the existence of a global solution of the Cauchy problem for the perturbation of the equilibrium state with periodic initial data. For the first time we calculate the stabilization speed to the equilibrium state (exponential stabilization).

Keywords: kinetic equation, Carleman equation, Fourier solution, equilibrium state, secular terms, generalized solution

DOI: https://doi.org/10.14498/vsgtu1529

Full text: PDF file (991 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 517.958:531.332
MSC: 35L45, 35L60, 35Q20
Received: January 21, 2017
Revised: February 25, 2017
Accepted: March 13, 2017
First online: May 11, 2017

Citation: S. A. Dukhnovskii, “On a speed of solutions stabilization of the Cauchy problem for the Carleman equation with periodic initial data”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 21:1 (2017), 7–41

Citation in format AMSBIB
\Bibitem{Duk17}
\by S.~A.~Dukhnovskii
\paper On a speed of solutions stabilization of the Cauchy problem for the Carleman equation with periodic initial data
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2017
\vol 21
\issue 1
\pages 7--41
\mathnet{http://mi.mathnet.ru/vsgtu1529}
\crossref{https://doi.org/10.14498/vsgtu1529}
\elib{https://elibrary.ru/item.asp?id=29245095}


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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. S. A. Dukhnovskii, “O skorosti stabilizatsii reshenii zadachi Koshi dlya sistemy uravnenii Godunova—Sultangazina s periodicheskimi nachalnymi dannymi”, Materialy IV Mezhdunarodnoi nauchnoi konferentsii “Aktualnye problemy prikladnoi matematiki”. Kabardino-Balkarskaya respublika, Nalchik, Prielbruse, 22–26 maya 2018 g. Chast I, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 165, VINITI RAN, M., 2019, 88–113  mathnet  crossref  mathscinet  elib
    2. S. A. Dukhnovskii, “Asymptotic stability of equilibrium states for Carleman and Godunov–Sultangazin systems of equations”, Moscow University Mathematics Bulletin, 74:6 (2019), 246–248  mathnet  crossref  isi
    3. S. A. Dukhnovskii, “Resheniya sistemy Karlemana cherez razlozhenie Penleve”, Vladikavk. matem. zhurn., 22:4 (2020), 58–67  mathnet  crossref  elib
    4. S. A. Dukhnovskii, “Global existence theorems of a solution of the Cauchy problem for systems of the kinetic Carleman and Godunov–Sultangazin equations”, Eurasian Math. J., 12:1 (2021), 97–102  mathnet  crossref
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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