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Mat. Sb., 2016, Volume 207, Number 10, Pages 4–27 (Mi msb8720)  

This article is cited in 2 scientific papers (total in 2 papers)

Local Petrovskii lacunas close to parabolic singular points of the wavefronts of strictly hyperbolic partial differential equations

V. A. Vassilievab

a National Research University "Higher School of Economics" (HSE), Moscow
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We enumerate the local Petrovskii lacunas (that is, the domains of local regularity of the principal fundamental solutions of strictly hyperbolic PDEs with constant coefficients in $\mathbb{R}^N$) close to parabolic singular points of their wavefronts (that is, at the points of types $P_8^1$, $P_8^2$, $\pm X_9$, $X_9^1$, $X_9^2$, $J_{10}^1$ and $J_{10}^3$). These points form the next most difficult family of classes in the natural classification of singular points after the so-called simple singularities $A_k$, $D_k$, $E_6$, $E_7$ and $E_8$, which have been investigated previously.
Also we present a computer program which counts the topologically distinct morsifications of critical points of smooth functions, and hence also the local components of the complement of a generic wavefront at its singular points.
Bibliography: 22 titles.

Keywords: wavefront, lacuna, hyperbolic operator, sharpness, morsification, Petrovskii cycle, Petrovskii criterion.

Funding Agency Grant Number
Russian Science Foundation 16-11-10316
Research was supported by a Russian Science Foundation grant (project no. 16-11-10316).


DOI: https://doi.org/10.4213/sm8720

Full text: PDF file (916 kB)
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English version:
Sbornik: Mathematics, 2016, 207:10, 1363–1383

Bibliographic databases:

ArXiv: 1607.04042
UDC: 517.955+515.16
MSC: Primary 35L30, 58G17; Secondary 38K40
Received: 20.04.2016 and 30.06.2016

Citation: V. A. Vassiliev, “Local Petrovskii lacunas close to parabolic singular points of the wavefronts of strictly hyperbolic partial differential equations”, Mat. Sb., 207:10 (2016), 4–27; Sb. Math., 207:10 (2016), 1363–1383

Citation in format AMSBIB
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\by V.~A.~Vassiliev
\paper Local Petrovskii lacunas close to parabolic singular points of the wavefronts of~strictly hyperbolic partial differential equations
\jour Mat. Sb.
\yr 2016
\vol 207
\issue 10
\pages 4--27
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\crossref{https://doi.org/10.4213/sm8720}
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\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2016SbMat.207.1363V}
\elib{https://elibrary.ru/item.asp?id=27350032}
\transl
\jour Sb. Math.
\yr 2016
\vol 207
\issue 10
\pages 1363--1383
\crossref{https://doi.org/10.1070/SM8720}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85007453511}


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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. V. V. Zharinov, “Hamiltonian operators in differential algebras”, Theoret. and Math. Phys., 193:3 (2017), 1725–1736  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. Victor A. Vassiliev, “New Examples of Irreducible Local Diffusion of Hyperbolic PDE's”, SIGMA, 16 (2020), 009, 21 pp.  mathnet  crossref  mathscinet
  • Математический сборник Sbornik: Mathematics (from 1967)
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