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Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 6, Pages 927–942 (Mi zvmmf10410)  

This article is cited in 2 scientific papers (total in 2 papers)

Boundary control problems for quasilinear systems of hyperbolic equations

A. E. Alekseenkoab, A. S. Kholodovab, Ya. A. Kholodovb

a Institute for Computer-Aided Design, Russian Academy of Sciences, Vtoraya Brestskaya ul. 19/18, Moscow, 123056, Russia
b Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia

Abstract: For quasilinear systems of hyperbolic equations, the nonclassical boundary value problem of controlling solutions with the help of boundary conditions is considered. Previously, this problem was extensively studied in the case of the simplest hyperbolic equations, namely, the scalar wave equation and certain linear systems. The corresponding problem formulations and numerical solution algorithms are extended to nonlinear (quasilinear and conservative) systems of hyperbolic equations. Some numerical (grid-characteristic) methods are considered that were previously used to solve the above problems. They include explicit and implicit conservative difference schemes on compact stencils that are linearizations of Godunov's method. The numerical algorithms and methods are tested as applied to well-known linear examples.

Key words: systems of hyperbolic equations, finite difference schemes, boundary control.

Funding Agency Grant Number
Russian Science Foundation 14-11-00877


DOI: https://doi.org/10.7868/S0044466916060168

Full text: PDF file (1916 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2016, 56:6, 916–931

Bibliographic databases:

UDC: 519.626
Received: 09.11.2015

Citation: A. E. Alekseenko, A. S. Kholodov, Ya. A. Kholodov, “Boundary control problems for quasilinear systems of hyperbolic equations”, Zh. Vychisl. Mat. Mat. Fiz., 56:6 (2016), 927–942; Comput. Math. Math. Phys., 56:6 (2016), 916–931

Citation in format AMSBIB
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\vol 56
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\pages 927--942
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\crossref{https://doi.org/10.7868/S0044466916060168}
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    This publication is cited in the following articles:
    1. A. V. Favorskaya, I. B. Petrov, “Theory and practice of wave processes modelling”, Innovations in Wave Processes Modelling and Decision Making: Grid-Characteristic Method and Applications, Smart Innovation Systems and Technologies, 90, eds. A. Favorskaya, I. Petrov, Springer-Verlag, Berlin, 2018, 1–6  crossref  mathscinet  isi  scopus
    2. Ya. A. Kholodov, “Razrabotka setevykh vychislitelnykh modelei dlya issledovaniya nelineinykh volnovykh protsessov na grafakh”, Kompyuternye issledovaniya i modelirovanie, 11:5 (2019), 777–814  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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