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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2002, Volume 236, Pages 120–133 (Mi tm282)  
This article is cited in 9 scientific papers (total in 9 papers)

Locally Bounded Generalized Entropy Solutions to the Cauchy Problem for a First-Order Quasilinear Equation

A. Yu. Goritskiia, E. Yu. Panovb

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Novgorod State University after Yaroslav the Wise
Full-text PDF (230 kB) Citations (9)
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Abstract: Generalized entropy solutions for a first-order quasilinear partial differential equation are studied. It is shown that the Cauchy problem for this equation is ill-posed in the class of locally bounded functions. The examples of nonexistence and nonuniqueness of solutions are constructed. Moreover, a uniqueness theorem, which holds for solutions integrable with respect to the spatial variable, is proved.
Received in December 2000
Bibliographic databases:
UDC: 517.95
Language: Russian
Citation: A. Yu. Goritskii, E. Yu. Panov, “Locally Bounded Generalized Entropy Solutions to the Cauchy Problem for a First-Order Quasilinear Equation”, Differential equations and dynamical systems, Collected papers. Dedicated to the 80th anniversary of academician Evgenii Frolovich Mishchenko, Trudy Mat. Inst. Steklova, 236, Nauka, MAIK «Nauka/Inteperiodika», M., 2002, 120–133; Proc. Steklov Inst. Math., 236 (2002), 110–123
Citation in format AMSBIB
\Bibitem{GorPan02}
\by A.~Yu.~Goritskii, E.~Yu.~Panov
\paper Locally Bounded Generalized Entropy Solutions to the Cauchy Problem for a~First-Order Quasilinear Equation
\inbook Differential equations and dynamical systems
\bookinfo Collected papers. Dedicated to the 80th anniversary of academician Evgenii Frolovich Mishchenko
\serial Trudy Mat. Inst. Steklova
\yr 2002
\vol 236
\pages 120--133
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm282}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1931012}
\zmath{https://zbmath.org/?q=an:1021.35063}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2002
\vol 236
\pages 110--123
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    • This publication is cited in the following 9 articles:
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