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Rec. Math. [Mat. Sbornik] N.S., 1937, Volume 2(44), Number 5, Pages 815–870 (Mi msb5630)  

This article is cited in 23 scientific papers (total in 23 papers)

Über das Cauchysche Problem für Systeme von partiellen Differentialgleichungen

I. Petrowsky

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Received: 14.01.1937
Language: German

Citation: I. Petrowsky, “Über das Cauchysche Problem für Systeme von partiellen Differentialgleichungen”, Rec. Math. [Mat. Sbornik] N.S., 2(44):5 (1937), 815–870

Citation in format AMSBIB
\by I.~Petrowsky
\paper \"Uber das Cauchysche Problem f\"ur Systeme von partiellen Differentialgleichungen
\jour Rec. Math. [Mat. Sbornik] N.S.
\yr 1937
\vol 2(44)
\issue 5
\pages 815--870

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    This publication is cited in the following articles:
    1. M. S. Agranovich, “Boundary value problrms for systems of first order pseudodifferential operators”, Russian Math. Surveys, 24:1 (1969), 59–126  mathnet  crossref  mathscinet  zmath
    2. J. Lions, “Partial differential inequalities”, Russian Math. Surveys, 27:2 (1972), 91–159  mathnet  crossref  mathscinet  zmath
    3. M. S. Agranovich, “Boundary value problems for systems with a parameter”, Math. USSR-Sb., 13:1 (1971), 25–64  mathnet  crossref  mathscinet  zmath
    4. L. R. Volevich, S. G. Gindikin, “The cauchy problem and other related problems for convolution equations”, Russian Math. Surveys, 27:4 (1972), 71–160  mathnet  crossref  mathscinet  zmath
    5. O. A. Oleinik, E. V. Radkevich, “Ob odnom klasse lineinykh differentsialnykh uravnenii, imeyuschikh neanaliticheskie resheniya”, UMN, 28:3(171) (1973), 191–192  mathnet  mathscinet  zmath
    6. J. Leray, “The linear analytic cauchy problem with singular initial data (after hamada and wagschal); partial hyperbolicity”, Russian Math. Surveys, 29:2 (1974), 213–222  mathnet  crossref  mathscinet  zmath
    7. Y. Choquet-Bruhat, “The stability of the solutions of non-linear hyperbolic equations on a manifold”, Russian Math. Surveys, 29:2 (1974), 327–335  mathnet  crossref  mathscinet  zmath
    8. V. Ya. Ivrii, V. M. Petkov, “Necessary conditions for the Cauchy problem for non-strictly hyperbolic equations to be well-posed”, Russian Math. Surveys, 29:5 (1974), 1–70  mathnet  crossref  mathscinet  zmath
    9. A. V. Fursikov, “Formuly dlya nekotorykh funktsionalov ot gladkikh reshenii odnogo klassa sistem kvazilineinykh uravnenii”, UMN, 31:1(187) (1976), 265–266  mathnet  mathscinet  zmath
    10. M. V. Fedoryuk, “Of Fourier integral operators and the asymptotic behaviour of the solution of the mixed problem”, Russian Math. Surveys, 32:6 (1977), 67–120  mathnet  crossref  mathscinet  zmath
    11. Yu. A. Dubinskii, “The algebra of pseudodifferential operators with analytic symbols and its applications to mathematical physics”, Russian Math. Surveys, 37:5 (1982), 109–153  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    12. A. Yu. Shcheglov, “A method for approximate solution in $C^2$ of a hyperbolic equation with Lipschitz nonlinearity”, Comput. Math. Math. Phys., 41:3 (2001), 392–406  mathnet  mathscinet  zmath  elib
    13. M. V. Falaleev, N. A. Sidorov, “Continuous and generalized solutions of singular partial differential equations”, Lobachevskii J. Math., 20 (2005), 31–45  mathnet  mathscinet  zmath  elib
    14. I. Ya. Aref'eva, I. V. Volovich, T. Ishiwatari, “Cauchy problem on non-globally hyperbolic space-times”, Theoret. and Math. Phys., 157:3 (2008), 1646–1654  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    15. I. V. Volovich, O. V. Groshev, N. A. Gusev, E. A. Kuryanovich, “On Solutions to the Wave Equation on a Non-globally Hyperbolic Manifold”, Proc. Steklov Inst. Math., 265 (2009), 262–275  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    16. V. I. Korzyuk, O. A. Konopel'ko, E. S. Cheb, “Boundary-value problems for fourth-order equations of hyperbolic and composite types”, Journal of Mathematical Sciences, 171:1 (2010), 89–115  mathnet  crossref  mathscinet  isi
    17. O. V. Groshev, “Existence and uniqueness of classical solutions of the Cauchy problem on nonglobally hyperbolic manifolds”, Theoret. and Math. Phys., 164:3 (2010), 1202–1207  mathnet  crossref  crossref  adsnasa  isi
    18. O. V. Groshev, “Zadacha Koshi dlya volnovogo uravneniya na neglobalno giperbolicheskikh mnogoobraziyakh”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(22) (2011), 42–46  mathnet  crossref  elib
    19. Mamchuev M.O., “Zadacha koshi v nelokalnoi postanovke dlya sistemy uravnenii s chastnymi proizvodnymi drobnogo poryadka”, Differentsialnye uravneniya, 48:3 (2012), 351–351  elib
    20. Korzyuk V.I., Kozlovskaya I.S., “Reshenie zadachi koshi dlya giperbolicheskogo uravneniya s postoyannymi koeffitsientami v sluchae dvukh nezavisimykh peremennykh”, Differentsialnye uravneniya, 48:5 (2012), 700–700  elib
    21. Mamchuev M.O., “Cauchy Problem in Nonlocal Statement for a System of Fractional Partial Differential Equations”, Differ. Equ., 48:3 (2012), 354–361  crossref  isi
    22. N. A. Sidorov, M. V. Falaleev, “Continuous and generalized solutions of singular integro-differential equations in Banach spaces”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2012, no. 11, 62–74  mathnet
    23. V. N. Margaryan, H. G. Ghazaryan, “On fundamental solutions of a class of weak hyperbolic operators”, Eurasian Math. J., 9:2 (2018), 54–67  mathnet
  • Математический сборник (новая серия) - 1936–1946
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