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Izvestiya: Mathematics, 1997, Volume 61, Issue 5, Pages 1069–1111
DOI: https://doi.org/10.1070/IM1997v061n05ABEH000163 (Mi im163) 		 
This article is cited in 7 scientific papers (total in 7 papers)

On the global solubility of the Monge–Ampere hyperbolic equations

D. V. Tunitsky

International Center "Sophus Lie"
English version PDF (346 kB) Citations (7)
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DOI: https://doi.org/10.1070/IM1997v061n05ABEH000163
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.
Received: 20.03.1996
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 1997, Volume 61, Issue 5, Pages 177–224
DOI: https://doi.org/10.4213/im163
Bibliographic databases:
MSC: 35L70
Language: English
Original paper language: Russian
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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\pages 177--224
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  • https://doi.org/10.1070/IM1997v061n05ABEH000163
  • https://www.mathnet.ru/eng/im/v61/i5/p177
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:486
    Russian version PDF:235
    English version PDF:21
    References:81
    First page:1
     
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