A. Kh. Khachatryan, Kh. A. Khachatryan, “Solvability of a nonlinear model Boltzmann equation in the problem of a plane shock wave”, TMF, 189:2 (2016), 239–255; Theoret. and Math. Phys., 189:2 (2016), 1609

Teoreticheskaya i Matematicheskaya Fizika

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

TMF:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 189, Number 2, Pages 239–255
DOI: https://doi.org/10.4213/tmf9108 (Mi tmf9108)

This article is cited in 23 scientific papers (total in 23 papers)

Solvability of a nonlinear model Boltzmann equation in the problem of a plane shock wave

A. Kh. Khachatryan^a, Kh. A. Khachatryan^b

^a Armenian State Agrarian University, Yerevan, Armenia
^b Institute of Mathematics, National Academy of Sciences of Armenia, Yerevan, Armenia

Full-text PDF (457 kB) Citations (23)

References:

PDF

HTML

DOI: https://doi.org/10.4213/tmf9108

Abstract: We consider a nonlinear system of integral equations describing the structure of a plane shock wave. Based on physical reasoning, we propose an iterative method for constructing an approximate solution of this system. The problem reduces to studying decoupled scalar nonlinear and linear integral equations for the gas temperature, density, and velocity. We formulate a theorem on the existence of a positive bounded solution of a nonlinear equation of the Uryson type. We also prove theorems on the existence and uniqueness of bounded positive solutions for linear integral equations in the space

L_{1} [- r, r]

$L_1[-r,r]$ for all finite

r < + \infty

$r<+\infty$ . For a more general nonlinear integral equation, we prove a theorem on the existence of a positive solution and also find a lower bound and an integral upper bound for the constructed solution.

Keywords: nonlinearity, shock wave, integral equation, bounded solution, iteration, pointwise convergence.

Funding agency	Grant number
State Committee on Science of the Ministry of Education and Science of the Republic of Armenia	SCS 15T-1A033
This research is supported by the State Science Committee, Ministry of Education and Science, Republic of Armenia (Project No. SCS 15T-1A033).

Received: 14.12.2015
Revised: 29.01.2016

English version:
Theoretical and Mathematical Physics, 2016, Volume 189, Issue 2, Pages 1609–1623
DOI: https://doi.org/10.1134/S0040577916110064

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: A. Kh. Khachatryan, Kh. A. Khachatryan, “Solvability of a nonlinear model Boltzmann equation in the problem of a plane shock wave”, TMF, 189:2 (2016), 239–255; Theoret. and Math. Phys., 189:2 (2016), 1609–1623

Citation in format AMSBIB

\Bibitem{KhaKha16}

\by A.~Kh.~Khachatryan, Kh.~A.~Khachatryan

\paper Solvability of a~nonlinear model Boltzmann equation in the~problem of a~plane shock wave

\jour TMF

\yr 2016

\vol 189

\issue 2

\pages 239--255

\mathnet{http://mi.mathnet.ru/tmf9108}

\crossref{https://doi.org/10.4213/tmf9108}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3589032}

\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2016TMP...189.1609K}

\elib{https://elibrary.ru/item.asp?id=27485054}

\transl

\jour Theoret. and Math. Phys.

\yr 2016

\vol 189

\issue 2

\pages 1609--1623

\crossref{https://doi.org/10.1134/S0040577916110064}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000389995500006}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85002998681}

Linking options:

https://www.mathnet.ru/eng/tmf9108

https://doi.org/10.4213/tmf9108

https://www.mathnet.ru/eng/tmf/v189/i2/p239

This publication is cited in the following 23 articles:

A. Kh. Khachatryan, Kh. A. Khachatryan, H. S. Petrosyan, “Solvability of a system of nonlinear integral equations on the entire line”, Complex Variables and Elliptic Equations, 2025, 1
A. Kh. Khachatryan, Kh. A. Khachatryan, A. S. Petrosyan, “Voprosy suschestvovaniya, otsutstviya i edinstvennosti resheniya odnogo klassa nelineinykh integralnykh uravnenii na vsei pryamoi s operatorom tipa Gammershteina — Ctiltesa”, Tr. IMM UrO RAN, 30, no. 1, 2024, 249–269
Kh. A. Khachatryan, H. S. Petrosyan, “Asymptotic Behavior of the Solution for One Class of Nonlinear Integral Equations of Hammerstein Type on the Whole Axis”, J Math Sci, 282:2 (2024), 292
Kh. A. Khachatryan, H. S. Petrosyan, “Constructive study of the solvability of one class of nonlinear integral equations with a symmetric kernel”, Siberian Adv. Math., 34:4 (2024), 320–336
H. S. Petrosyan, Kh. A. Khachatryan, “Uniqueness of the Solution of a Class of Integral Equations with Sum-Difference. Kernel and with Convex Nonlinearity on the Positive Half-Line”, Math. Notes, 113:4 (2023), 512–524
Kh. A. Khachatryan, H. S. Petrosyan, “On non-trivial solvability of one system of non-linear integral equations on the real axis”, Izv. Math., 87:5 (2023), 1062–1077
Kh. A. Khachatryan, H. S. Petrosyan, A. R. Hakobyan, “On some systems of nonlinear integral equations on the whole axis with monotonous Hammerstein–Volterra type operators”, Eurasian Math. J., 14:3 (2023), 35–53
A. A. Davydov, Kh. A. Khachatryan, A. S. Petrosyan, “On Solutions of a System of Nonlinear Integral Equations of Convolution Type on the Entire Real Line”, Differentsialnye uravneniya, 59:11 (2023), 1500
A.Kh. Khachatryan, Kh.A. Khachatryan, “ON QUALITATIVE PROPERTIES OF A SOLUTION OF ONE CLASS SINGULAR INTEGRAL EQUATIONS ON THE WHOLE LINE WITH ODD NONLINEARITY”, J Math Sci, 271:5 (2023), 597
A. A. Davydov, Kh. A. Khachatryan, H. S. Petrosyan, “On Solutions of a System of Nonlinear Integral Equations of Convolution Type on the Entire Real Line”, Diff Equat, 59:11 (2023), 1504
Kh. A. Khachatryan, A. S. Petrosyan, “Asimptoticheskoe povedenie resheniya dlya odnogo klassa nelineinykh integralnykh uravnenii tipa Gammershteina na vsei pryamoi”, SMFN, 68, no. 2, Rossiiskii universitet druzhby narodov, M., 2022, 376–391
Kh. A. Khachatryan, A. S. Petrosyan, “Voprosy suschestvovaniya i edinstvennosti resheniya odnogo klassa nelineinykh integralnykh uravnenii na vsei pryamoi”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 26:3 (2022) (to appear)
Kh. A. Khachatryan, A. S. Petrosyan, “Voprosy suschestvovaniya i edinstvennosti resheniya odnogo klassa nelineinykh integralnykh uravnenii na vsei pryamoi”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 26:3 (2022), 446–479
Kh. A. Khachatryan, H. S. Petrosyan, S. M. Andriyan, “On the solubility of a class of two-dimensional integral equations on a quarter plane with monotone nonlinearity”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2022, no. 2, 19–38
A. Kh. Khachatryan, Kh. A. Khachatryan, “Ob odnoi sisteme integralnykh uravnenii na vsei pryamoi s vypukloi i monotonnoi nelineinostyu”, Proceedings of NAS RA. Mathematics, 2022, 65
A. Kh. Khachatryan, Kh. A. Khachatryan, “A System of Integral Equations on the Entire Axis with Convex and Monotone Nonlinearity”, J. Contemp. Mathemat. Anal., 57:5 (2022), 311
Kh. A. Khachatryan, H. S. Petrosyan, “On a class of convolution type nonlinear integral equations with an even kernel”, Int. J. Mod. Phys. A, 37:20n21 (2022)
Kh. A. Khachatryan, H. S. Petrosyan, “On One Class of Multidimensional Integral Equations of Convolution Type with Convex Nonlinearity”, Diff Equat, 58:5 (2022), 680
A. Kh. Khachatryan, Kh. A. Khachatryan, H. S. Petrosyan, “On positive bounded solutions of one class of nonlinear integral equations with the Hammerstein-Nemytskii operator”, Differ. Equ., 57:6 (2021), 768–779
Kh. A. Khachatryan, “Existence and uniqueness of solution of a certain boundary-value problem for a convolution integral equation with monotone non-linearity”, Izv. Math., 84:4 (2020), 807–815

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

Statistics & downloads:
Abstract page:	777
Full-text PDF :	160
References:	69
First page:	18

Registration to the website

Logotypes