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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 3, Pages 450–462 (Mi zvmmf10006)  

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

On the asymptotics of the solution to a singularly perturbed hyperbolic system of equations with several spatial variables in the critical case

T. V. Pavlyukab, A. V. Nesterovba

a Obninsk State Technical University for Nuclear Power Engineering, National Research Nuclear University УMEPhIФ, Studgorodok 1, Obninsk, Kaluga oblast, 249040, Russia
b Moscow City Pedagogical University, Vtoroi SelТskokhozyaistvennyi pr. 4, Moscow, 129226, Russia

Abstract: A complete asymptotic expansion of the solution to an initial value problem for a singularly perturbed hyperbolic system of equations in several spatial variables is constructed and justified. A specific feature of the problem is that its solution has a spike zone in a neighborhood of which the asymptotics is described by a parabolic equation.

Key words: small parameter, singular perturbations, initial-boundary value problems, hyperbolic systems, asymptotic representation of solutions, spike function.

DOI: https://doi.org/10.7868/S0044466914030168

Full text: PDF file (252 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:3, 462–473

Bibliographic databases:

UDC: 519.633
Received: 14.04.2014

Citation: T. V. Pavlyuk, A. V. Nesterov, “On the asymptotics of the solution to a singularly perturbed hyperbolic system of equations with several spatial variables in the critical case”, Zh. Vychisl. Mat. Mat. Fiz., 54:3 (2014), 450–462; Comput. Math. Math. Phys., 54:3 (2014), 462–473

Citation in format AMSBIB
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\pages 450--462
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    Erratum

    This publication is cited in the following articles:
    1. A. V. Nesterov, “On the structure of solutions of a class of hyperbolic systems with several spatial variables in the far field”, Comput. Math. Math. Phys., 56:4 (2016), 626–636  mathnet  crossref  crossref  mathscinet  isi  elib
  • ∆урнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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