This article is cited in 3 scientific papers (total in 3 papers)
Evolution of Lagrangian Manifolds and Asymptotic Solutions to the Linearized Equations of Gas Dynamics
Anna I. Alliluevaabc, Andrei I. Shafarevichcbad
a National Research Centre “Kurchatov Institute”, pl. Akademika Kurchatova 1, Moscow, 123182 Russia
b Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, 141700 Russia
c Institute for Problems in Mechanics, pr. Vernadskogo 101-1, Moscow, 119526 Russia
d M. V. Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991 Russia
We study asymptotic solution of the Cauchy problem for linearized equations of gas dynamics with rapidly oscillating initial data. We construct the formal serie, satisfying this problem. This serie is naturally divided into three parts, corresponding to the hydrodynamic mode and two acoustic modes. The summands of the serie are expressed in terms of the Maslov canonic operator on moving Lagrangian manifolds. Evolution of the manifolds is governed by the corresponding classical Hamiltonian systems.
Lagrangian manifolds, short-wave asymptotics, equations of gas dynamics
|Russian Science Foundation
|This work was supported by the Russian Science Foundation (grant 16-11-10282).
MSC: 53C56, 35P20
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
Citation in format AMSBIB
\by Anna I. Allilueva, Andrei I. Shafarevich
\paper Evolution of Lagrangian Manifolds and Asymptotic Solutions to the Linearized Equations of Gas Dynamics
\jour Regul. Chaotic Dyn.
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This publication is cited in the following articles:
Allilueva A.I., Shafarevich A.I., “Localized Asymptotic Solutions of Linearized Equations of Gas Dynamics”, Russ. J. Math. Phys., 25:4 (2018), 415–422
Anna I. Allilueva, Andrei I. Shafarevich, “Conic Lagrangian Varieties and Localized Asymptotic Solutions of Linearized Equations of Relativistic Gas Dynamics”, Regul. Chaotic Dyn., 24:6 (2019), 671–681
Allilueva A.I., Shafarevich A.I., “Short-Wave Asymptotic Solutions of a Linearized System of Relativistic Gas Dynamics”, Russ. J. Math. Phys., 26:3 (2019), 255–264
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