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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2003, Volume 243, Pages 257–288 (Mi tm433)  
This article is cited in 4 scientific papers (total in 5 papers)

On a priori Estimates and Gradient Catastrophes of Smooth Solutions to Hyperbolic Systems of Conservation Laws

S. I. Pokhozhaev

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (342 kB) Citations (5)
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Abstract: This paper is devoted to a priori estimates and blow-up of global smooth solutions to the Cauchy problem for nonlinear hyperbolic systems of conservation laws. A general approach is proposed to obtain integral a priori estimates for smooth solutions of such systems. An application to a system of equations for one-dimensional nonisentropic and isentropic flows of a polytropic gas is considered. Integral conditions for the initial data are found that give rise to the gradient catastrophe of such solutions.
Received in March 2003
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: S. I. Pokhozhaev, “On a priori Estimates and Gradient Catastrophes of Smooth Solutions to Hyperbolic Systems of Conservation Laws”, Function spaces, approximations, and differential equations, Collected papers. Dedicated to the 70th birthday of Oleg Vladimirovich Besov, corresponding member of RAS, Trudy Mat. Inst. Steklova, 243, Nauka, MAIK «Nauka/Inteperiodika», M., 2003, 257–288; Proc. Steklov Inst. Math., 243 (2003), 247–277
Citation in format AMSBIB
\Bibitem{Pok03}
\by S.~I.~Pokhozhaev
\paper On a~priori Estimates and Gradient Catastrophes of Smooth Solutions to Hyperbolic Systems of Conservation Laws
\inbook Function spaces, approximations, and differential equations
\bookinfo Collected papers. Dedicated to the 70th birthday of Oleg Vladimirovich Besov, corresponding member of RAS
\serial Trudy Mat. Inst. Steklova
\yr 2003
\vol 243
\pages 257--288
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm433}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2054438}
\zmath{https://zbmath.org/?q=an:1077.35093}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2003
\vol 243
\pages 247--277
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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