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Mat. Zametki, 2012, Volume 92, Issue 1, Pages 153–156 (Mi mz9488)  

This article is cited in 12 scientific papers (total in 12 papers)

Brief Communications

Phase Space Geometry for a Wave Equation Degenerating on the Boundary of the Domain

V. E. Nazaikinskiiabc

a A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences
b Moscow Institute of Physics and Technology
c Moscow State Institute of Electronics and Mathematics (Technical University)

Keywords: wave equation, degeneration, run-up, tsunami wave, phase space geometry

DOI: https://doi.org/10.4213/mzm9488

Full text: PDF file (346 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2012, 92:1, 144–148

Bibliographic databases:

Received: 13.12.2011
Revised: 27.02.2012

Citation: V. E. Nazaikinskii, “Phase Space Geometry for a Wave Equation Degenerating on the Boundary of the Domain”, Mat. Zametki, 92:1 (2012), 153–156; Math. Notes, 92:1 (2012), 144–148

Citation in format AMSBIB
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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. P. A. Sipailo, “On the numerical simulation of the propagation of the wave front of a tsunami wave in a pool of variable depth with run-up on the beach”, Russ. J. Math. Phys., 20:3 (2013), 383–386  crossref  mathscinet  zmath  isi  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
    3. V. E. Nazaikinskii, “The Maslov Canonical Operator on Lagrangian Manifolds in the Phase Space Corresponding to a Wave Equation Degenerating on the Boundary”, Math. Notes, 96:2 (2014), 248–260  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. V. E. Nazaikinskii, “Maslov's canonical operator for degenerate hyperbolic equations”, Russ. J. Math. Phys., 21:2 (2014), 289–290  crossref  mathscinet  zmath  isi
    5. S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Characteristics with Singularities and the Boundary Values of the Asymptotic Solution of the Cauchy Problem for a Degenerate Wave Equation”, Math. Notes, 100:5 (2016), 695–713  mathnet  crossref  crossref  mathscinet  isi  elib
    6. S. A. Sergeev, A. A. Tolchennikov, “Creation Operators in the Problem of Localized Solutions of the Linearized Shallow Water Equations with Regular and Singular Characteristics”, Math. Notes, 100:6 (2016), 852–861  mathnet  crossref  crossref  mathscinet  isi  elib
    7. D. A. Lozhnikov, V. E. Nazaikinskii, “Method for the analysis of long water waves taking into account reflection from a gently sloping beach”, Pmm-J. Appl. Math. Mech., 81:1 (2017), 21–28  crossref  mathscinet  isi
    8. A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Simple Asymptotics for a Generalized Wave Equation with Degenerating Velocity and Their Applications in the Linear Long Wave Run-Up Problem”, Math. Notes, 104:4 (2018), 471–488  mathnet  crossref  crossref  isi  elib
    9. Anatoly Anikin, Sergey Dobrokhotov, Vladimir Nazaikinskii, “Asymptotic solutions of the wave equation with degenerate velocity and with right-hand side localized in space and time”, Zhurn. matem. fiz., anal., geom., 14:4 (2018), 393–405  mathnet  crossref
    10. 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
    11. A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. V. Tsvetkova, “Asimptotiki sobstvennykh funktsii dvumernogo operatora $\nabla D(x)\nabla$, svyazannye s bilyardami s poluzhestkimi stenkami, i zakhvachennye beregovye volny”, Matem. zametki, 105:5 (2019), 792–797  mathnet  crossref  elib
    12. Anikin A.Yu. Dobrokhotov S.Yu. Nazaikinskii V.E. Tsvetkova A.V., “Asymptotic Eigenfunctions of the Operator Delta D(X)Delta Defined in a Two-Dimensional Domain and Degenerating on Its Boundary and Billiards With Semi-Rigid Walls”, Differ. Equ., 55:5 (2019), 644–657  crossref  isi
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