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Mat. Zametki, 2012, Volume 92, Issue 5, Pages 721–730 (Mi mz10129)  

This article is cited in 8 scientific papers (total in 8 papers)

Asymptotics of the Solutions of the One-Dimensional Nonlinear System of Equations of Shallow Water with Degenerate Velocity

D. S. Minenkov

A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences

Abstract: A system of one-dimensional nonlinear equations of shallow water with degenerate velocity is considered. The change of variables taking the given system to a nonlinear system with small nonlinearity is proposed. Formal asymptotic solutions near the point of degeneracy are obtained.

Keywords: nonlinear system of equations of shallow water, Carrier–Greenspan transformation, Cauchy problem, Schwartz space, Duhamel integral, Hankel transform

DOI: https://doi.org/10.4213/mzm10129

Full text: PDF file (527 kB)
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English version:
Mathematical Notes, 2012, 92:5, 664–672

Bibliographic databases:

UDC: 517.95
Received: 20.02.2012

Citation: D. S. Minenkov, “Asymptotics of the Solutions of the One-Dimensional Nonlinear System of Equations of Shallow Water with Degenerate Velocity”, Mat. Zametki, 92:5 (2012), 721–730; Math. Notes, 92:5 (2012), 664–672

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. Yu. Dobrokhotov, S. B. Medvedev, D. S. Minenkov, “On Replacements Reducing One-Dimensional Systems of Shallow-Water Equations to the Wave Equation with Sound Speed $c^2=x$”, Math. Notes, 93:5 (2013), 704–714  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. S. Yu. Dobrokhotov, V. E. Nazaikinskii, B. Tirozzi, “Two-dimensional wave equation with degeneration on the curvilinear boundary of the domain and asymptotic solutions with localized initial data”, Russ. J. Math. Phys., 20:4 (2013), 389–401  crossref  mathscinet  zmath  isi  scopus
    3. Yu. A. Chirkunov, S. Yu. Dobrokhotov, S. B. Medvedev, D. S. Minenkov, “Exact solutions of one-dimensional nonlinear shallow water equations over even and sloping bottoms”, Theoret. and Math. Phys., 178:3 (2014), 278–298  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. V. P. Maslov, “New construction of classical thermodynamics and UD-statistics”, Russ. J. Math. Phys., 21:2 (2014), 256–284  crossref  mathscinet  zmath  isi  scopus
    5. V. P. Maslov, “Two-fluid picture of supercritical phenomena”, Theoret. and Math. Phys., 180:3 (2014), 1096–1129  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    6. Dynnikov I.A., Mironov A.E., Taimanov I.A., Vesnin A.Yu., “The Conference ‘’Dynamics in Siberia", Novosibirsk, February 29 - March 4, 2016”, Sib. Electron. Math. Rep., 13 (2016), A1–A41  mathnet  crossref  mathscinet  isi
    7. Minenkov D.S., “Asymptotics Near the Shore For 2D Shallow Water Over Sloping Planar Bottom”, Proceedings of the International Conference Days on Diffraction (Dd) 2017, ed. Motygin O. Kiselev A. Goray L. Suslina T. Kazakov A. Kirpichnikova A., IEEE, 2017, 240–243  isi
    8. Dobrokhotov S.Yu. Nazaikinskii V.E., “Asymptotic Localized Solutions of the Shallow Water Equations Over a Nonuniform Bottom”, AIP Conference Proceedings, 2048, ed. Pasheva V. Popivanov N. Venkov G., Amer Inst Physics, 2018, 040026  crossref  isi
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