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Recueil Mathématique (Nouvelle série), 1945, Volume 17(59), Number 3, Pages 289–370 (Mi sm6354)  

This article is cited in 19 scientific papers (total in 20 papers)

On the diffusion of waves and the lacunas for hyperbolic equations

I. Petrowsky
Received: 12.04.1945
Bibliographic databases:
Language: English
Citation: I. Petrowsky, “On the diffusion of waves and the lacunas for hyperbolic equations”, Sb. Math., 59:3 (1945)
Citation in format AMSBIB
\Bibitem{Pet45}
\by I.~Petrowsky
\paper On the diffusion of waves and the lacunas for hyperbolic equations
\jour Sb. Math.
\yr 1945
\vol 59
\issue 3
\mathnet{http://mi.mathnet.ru/eng/sm6354}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=16861}
\zmath{https://zbmath.org/?q=an:0061.21309}
Linking options:
  • https://www.mathnet.ru/eng/sm6354
  • https://www.mathnet.ru/eng/sm/v59/i3/p289
  • This publication is cited in the following 20 articles:
    1. V. I. Korzyuk, Ya. V. Rudko, “Klassicheskoe reshenie zadachi Koshi dlya polulineinogo giperbolicheskogo uravneniya v sluchae dvukh nezavisimykh peremennykh”, Izv. vuzov. Matem., 2024, no. 3, 50–63  mathnet  crossref
    2. V. A. Vassiliev, “Complements of discriminants of real parabolic function singularities”, Mosc. Math. J., 23:3 (2023), 401–432  mathnet
    3. Victor A. Vassiliev, “New Examples of Irreducible Local Diffusion of Hyperbolic PDE's”, SIGMA, 16 (2020), 009, 21 pp.  mathnet  crossref  mathscinet
    4. V. A. Vassiliev, “New Examples of Locally Algebraically Integrable Bodies”, Math. Notes, 106:6 (2019), 894–898  mathnet  crossref  crossref  mathscinet  isi  elib
    5. V. P. Palamodov, “New approaches to inverse scattering”, Russian Math. Surveys, 71:3 (2016), 513–537  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. V. A. Vassiliev, “Local Petrovskii lacunas close to parabolic singular points of the wavefronts of strictly hyperbolic partial differential equations”, Sb. Math., 207:10 (2016), 1363–1383  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. Hayrapetyan S.R., Margaryan V.N., “Estimation of Higher Derivatives of the Solutions for a Class of Almost Hypoelliptic Equations in an Infinite Strip”, J. Contemp. Math. Anal.-Armen. Aca., 45:5 (2010), 293–303  crossref  isi
    8. V. I. Arnol'd, “I. G. Petrovskii, Hilbert's topological problems, and modern mathematics”, Russian Math. Surveys, 57:4 (2002), 833–845  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    9. Yu. Yu. Berest, A. P. Veselov, “Huygens' principle and integrability”, Russian Math. Surveys, 49:6 (1994), 5–77  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    10. V. A. Vassiliev, “Geometry of local lacunae of hyperbolic operators with constant coefficients”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 111–123  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    11. N. Kh. Ibragimov, A. O. Oganesyan, “The hierarchy of Huygens equations in spaces with a non-trivial conformal group”, Russian Math. Surveys, 46:3 (1991), 137–176  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    12. A. N. Varchenko, “On normal forms of nonsmoothness of solutions of hyperbolic equations”, Math. USSR-Izv., 30:3 (1988), 615–628  mathnet  crossref  mathscinet  zmath
    13. V. A. Vassiliev, “Sharpness and the local Petrovskii condition for strictly hyperbolic operators with constant coefficients”, Math. USSR-Izv., 28:2 (1987), 233–273  mathnet  crossref  mathscinet  zmath
    14. O. Ya. Viro, “Progress in the topology of real algebraic varieties over the last six years”, Russian Math. Surveys, 41:3 (1986), 55–82  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    15. M. F. Atya, R. Bott, L. Gording, “Lakuny dlya giperbolicheskikh differentsialnykh operatorov s postoyannymi koeffitsientami. II”, UMN, 39:3(237) (1984), 171–224  mathnet  mathscinet  zmath
    16. L. Gording, “Rezkie fronty parnykh ostsilliruyuschikh integralov”, UMN, 38:6(234) (1983), 85–96  mathnet  mathscinet  zmath
    17. I. A. Kipriyanov, L. A. Ivanov, “On lacunae for some classes of equations with singularities”, Math. USSR-Sb., 38:2 (1981), 217–230  mathnet  crossref  mathscinet  zmath  isi
    18. S. A. Gal'pern, “Fundamental solutions and lacunae of quasihyperbolic equations”, Russian Math. Surveys, 29:2 (1974), 158–169  mathnet  crossref  mathscinet  zmath
    19. M. F. Atya, R. Bott, L. Gording, “Lakuny dlya giperbolicheskikh differentsialnykh operatorov s postoyannymi koeffitsientami. I”, UMN, 26:2(158) (1971), 25–100  mathnet  mathscinet  zmath
    20. L. Gording, “Rezkie fronty i lakuny”, UMN, 26:2(158) (1971), 175–181  mathnet  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1936–1946 Sbornik: Mathematics
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