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TMF, 2017, Volume 190, Number 1, Pages 191–204 (Mi tmf9228)  

This article is cited in 6 scientific papers (total in 6 papers)

Nonstandard characteristics and localized asymptotic solutions of a linearized magnetohydrodynamic system with small viscosity and drag

A. I. Alliluevaabc, A. I. Shafarevichdabc

a Ishlinskii Institute for Mechanical Problems, RAS, Moscow, Russia
b Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Oblast, Russia
c National Research Centre "Kurchatov Institute", Moscow, Russia
d Lomonosov Moscow State University, Moscow, Russia

Abstract: We describe asymptotic solutions of the Cauchy problem for a linearized system of magnetohydrodynamics with initial conditions localized in a small neighborhood of a curve or a two-dimensional surface. We investigate how a change of the multiplicity of characteristics affects such solutions and prove a uniform estimate of the residual.

Keywords: magnetohydrodynamic equation, nonstandard characteristic

Funding Agency Grant Number
Russian Science Foundation 16-11-10282
This research is supported by a grant from the Russian Science Foundation (Project No. 16-11-10282).


DOI: https://doi.org/10.4213/tmf9228

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English version:
Theoretical and Mathematical Physics, 2017, 190:1, 164–175

Bibliographic databases:

Received: 16.05.2016

Citation: A. I. Allilueva, A. I. Shafarevich, “Nonstandard characteristics and localized asymptotic solutions of a linearized magnetohydrodynamic system with small viscosity and drag”, TMF, 190:1 (2017), 191–204; Theoret. and Math. Phys., 190:1 (2017), 164–175

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf9228
  • http://mi.mathnet.ru/eng/tmf/v190/i1/p191

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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. Allilueva A.I., Shafarevich A.I., “Asymptotic Support of Localized Solutions of the Linearized System of Magnetohydrodynamics”, Russ. J. Math. Phys., 23:4 (2016), 425–430  crossref  mathscinet  zmath  isi  scopus
    2. A. I. Allilueva, A. I. Shafarevich, “Localized Asymptotic Solutions of the Linearized System of Magnetic Hydrodynamics”, Math. Notes, 102:6 (2017), 737–745  mathnet  crossref  crossref  isi  elib
    3. A. I. Allilueva, A. I. Shafarevich, “Localized asymptotic solutions of linearized equations of gas dynamics”, Russ. J. Math. Phys., 25:4 (2018), 415–422  crossref  mathscinet  zmath  isi
    4. Anna I. Allilueva, Andrei I. Shafarevich, “Evolution of Lagrangian Manifolds and Asymptotic Solutions to the Linearized Equations of Gas Dynamics”, Regul. Chaotic Dyn., 24:1 (2019), 80–89  mathnet  crossref
    5. Allilueva I A., Shafarevich I A., “Localized Solutions For Linearized Mhd Equations and Interaction of Alfven Modes”, Magnetohydrodynamics, 55:1-2, SI (2019), 15–21  crossref  isi
    6. Allilueva A.I., Shafarevich A.I., “Double Asymptotic Expansion of the Resolving Operator of the Cauchy Problem For the Linearized System of Gas Dynamics”, Dokl. Math., 99:1 (2019), 16–19  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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