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Sbornik: Mathematics, 1997, Volume 188, Issue 1, Pages 87–113
DOI: https://doi.org/10.1070/sm1997v188n01ABEH000189 (Mi sm189) 		 
An approximation scheme for measure-valued solutions of a first-order quasilinear equation

E. Yu. Panov

Novgorod State University after Yaroslav the Wise
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DOI: https://doi.org/10.1070/sm1997v188n01ABEH000189
Abstract: A kinetic definition of a measure-valued solution of the Cauchy problem for a first-order quasilinear equation is presented. Using a suitable approximation of the right-hand side of the corresponding kinetic equation a family of equations is constructed. The unique solubility of Cauchy problems for these equations and the convergence (after possibly going over to a subsequence) of the resulting sequence of solutions to a generalized solution of the original problem are established.
Received: 06.02.1996
Russian version:
Matematicheskii Sbornik, 1997, Volume 188, Number 1, Pages 83–108
DOI: https://doi.org/10.4213/sm189
Bibliographic databases:
UDC: 517.95
MSC: 35D99, 35F20
Language: English
Original paper language: Russian
Citation: E. Yu. Panov, “An approximation scheme for measure-valued solutions of a first-order quasilinear equation”, Mat. Sb., 188:1 (1997), 83–108; Sb. Math., 188:1 (1997), 87–113
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v188/i1/p83
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    Abstract page:348
    Russian version PDF:183
    English version PDF:12
    References:56
    First page:1
     
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