Email this article Evolution of Lagrangian Manifolds and Asymptotic Solutions to the Linearized Equations of Gas Dynamics
- Authors: Allilueva A.I.1,2,3, Shafarevich A.I.1,2,3,4
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Affiliations:
- Institute for Problems in Mechanics
- Moscow Institute of Physics and Technology
- National Research Centre “Kurchatov Institute”
- M. V. Lomonosov Moscow State University
- Issue: Vol 24, No 1 (2019)
- Pages: 80-89
- Section: Article
- URL: https://ogarev-online.ru/1560-3547/article/view/219258
- DOI: https://doi.org/10.1134/S1560354719010040
- ID: 219258
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Abstract
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.
About the authors
Anna I. Allilueva
Institute for Problems in Mechanics; Moscow Institute of Physics and Technology; National Research Centre “Kurchatov Institute”
Author for correspondence.
Email: esina_anna@list.ru
Russian Federation, pr. Vernadskogo 101-1, Moscow, 119526; Institutskii per. 9, Dolgoprudnyi, 141700; pl. Akademika Kurchatova 1, Moscow, 123182
Andrei I. Shafarevich
Institute for Problems in Mechanics; Moscow Institute of Physics and Technology; National Research Centre “Kurchatov Institute”; M. V. Lomonosov Moscow State University
Email: esina_anna@list.ru
Russian Federation, pr. Vernadskogo 101-1, Moscow, 119526; Institutskii per. 9, Dolgoprudnyi, 141700; pl. Akademika Kurchatova 1, Moscow, 123182; Leninskie Gory 1, Moscow, 119991
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