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Izv. RAN. Ser. Mat., 1997, Volume 61, Issue 5, Pages 177–224 (Mi izv163)  

This article is cited in 3 scientific papers (total in 3 papers)

On the global solubility of the Monge–Ampere hyperbolic equations

D. V. Tunitsky

International Center "Sophus Lie"

Abstract: This paper is devoted to the solubility of the Cauchy problem for the Monge–Ampere hyperbolic equations, in particular, for quasi-linear equations with two independent variables. It is proved that this problem has a unique maximal solution in the class of multi-valued solutions. The notion of a multi-valued solution goes back to Monge, Lie, et al. It is an historical predecessor of the notion of a generalized solution in the Sobolev–Schwartz sense. The relationship between multi-valued and generalized solutions of linear differential equations is established.

DOI: https://doi.org/10.4213/im163

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English version:
Izvestiya: Mathematics, 1997, 61:5, 1069–1111

Bibliographic databases:

MSC: 35L70
Received: 20.03.1996

Citation: D. V. Tunitsky, “On the global solubility of the Monge–Ampere hyperbolic equations”, Izv. RAN. Ser. Mat., 61:5 (1997), 177–224; Izv. Math., 61:5 (1997), 1069–1111

Citation in format AMSBIB
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\by D.~V.~Tunitsky
\paper On the global solubility of the Monge--Ampere hyperbolic equations
\jour Izv. RAN. Ser. Mat.
\yr 1997
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\pages 177--224
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\yr 1997
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\pages 1069--1111
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  • https://doi.org/10.4213/im163
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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. Vinogradov A.M., Marvan M., Yumaguzhin V.A., “Differential invariants of generic hyperbolic Monge-Ampere equations”, Doklady Mathematics, 72:3 (2005), 883–885  zmath  isi  elib
    2. Marvan, M, “Differential invariants of generic hyperbolic Monge-Ampere equations”, Central European Journal of Mathematics, 5:1 (2007), 105  crossref  mathscinet  zmath  isi  scopus
    3. D. V. Tunitsky, “On the global solubility of the Cauchy problem for hyperbolic Monge–Ampére systems”, Izv. Math., 82:5 (2018), 1019–1075  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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