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Izvestiya: Mathematics, 1996, Volume 60, Issue 2, Pages 335–377
DOI: https://doi.org/10.1070/IM1996v060n02ABEH000073 (Mi im73) 		 
This article is cited in 30 scientific papers (total in 30 papers)

On measure-valued solutions of the Cauchy problem for a first-order quasilinear equation

E. Yu. Panov

Novgorod State University after Yaroslav the Wise
English version PDF (1591 kB) Citations (30)
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DOI: https://doi.org/10.1070/IM1996v060n02ABEH000073
Abstract: Measure-valued solutions of the Cauchy problem are considered for a first-order quasilinear equation with only continuous flow functions. A measure-valued analogue of the maximum principle (in Lebesgue spaces) is proved. Conditions are found under which a measure-valued solution is an ordinary function. Uniqueness questions are studied. The class of “strong” measure-valued solutions is distinguished and the existence and uniqueness (under natural restrictions) of a strong measure-valued solution is proved. Questions of the convergence of sequences of measure-valued solutions are studied.
Received: 04.04.1995
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 1996, Volume 60, Issue 2, Pages 107–148
DOI: https://doi.org/10.4213/im73
Bibliographic databases:
UDC: 517.95
MSC: Primary 35L65, 35D05, 35D10; Secondary 49M30, 35F25
Language: English
Original paper language: Russian
Citation: E. Yu. Panov, “On measure-valued solutions of the Cauchy problem for a first-order quasilinear equation”, Izv. RAN. Ser. Mat., 60:2 (1996), 107–148; Izv. Math., 60:2 (1996), 335–377
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/im/v60/i2/p107
    • This publication is cited in the following 30 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:534
    Russian version PDF:225
    English version PDF:12
    References:88
    First page:1
     
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