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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 8, Pages 1394–1407 (Mi zvmmf11119)  

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

Efficient asymptotics in problems on the propagation of waves generated by localized sources in linear multidimensional inhomogeneous and dispersive media

S. Yu. Dobrokhotov, V. E. Nazaikinskii

Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia

Abstract: The Cauchy problem with localized initial conditions is considered for a large class of evolution equations that includes the Schrödinger and Dirac equations, Maxwell equations, linearized fluid dynamics equations, equations of the linear theory of surface water waves, equations of elasticity theory, acoustics equations, and many others. A general approach to the construction of efficient asymptotic formulas in such problems is discussed.

Key words: evolution equation, Cauchy problem, localized initial conditions, semiclassical asymptotics, WKB method, Maslov's canonical operator, efficient formulas.

Funding Agency
This paper is based on the studies supported by the Russian Science Foundation under project no. 16-11-10282.


DOI: https://doi.org/10.31857/S0044466920080062


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:8, 1348–1360

Bibliographic databases:

UDC: 517.9
Received: 15.02.2020
Revised: 15.02.2020
Accepted:09.04.2020

Citation: S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Efficient asymptotics in problems on the propagation of waves generated by localized sources in linear multidimensional inhomogeneous and dispersive media”, Zh. Vychisl. Mat. Mat. Fiz., 60:8 (2020), 1394–1407; Comput. Math. Math. Phys., 60:8 (2020), 1348–1360

Citation in format AMSBIB
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\paper Efficient asymptotics in problems on the propagation of waves generated by localized sources in linear multidimensional inhomogeneous and dispersive media
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2020
\vol 60
\issue 8
\pages 1394--1407
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\crossref{https://doi.org/10.31857/S0044466920080062}
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\transl
\jour Comput. Math. Math. Phys.
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\vol 60
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\pages 1348--1360
\crossref{https://doi.org/10.1134/S0965542520080060}
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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. S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich, “Effektivnye asimptotiki reshenii zadachi Koshi s lokalizovannymi nachalnymi dannymi dlya lineinykh sistem differentsialnykh i psevdodifferentsialnykh uravnenii”, UMN, 76:5(461) (2021), 3–80  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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