This article is cited in 5 scientific papers (total in 5 papers)
A non-local theory of generalized entropy solutions of the Cauchy problem for a class of hyperbolic systems of conservation laws
E. Yu. Panov
Novgorod State University after Yaroslav the
We consider a hyperbolic system of conservation laws on the space of symmetric second-order matrices. The right-hand side of this system contains the functional calculus
operator $\tilde f(U)$generated in the general case only by a continuous scalar
function $f(u)$. For these systems we define and describe the set of singular entropies, introduce the concept of generalized entropy solutions of the corresponding Cauchy problem, and investigate the properties of generalized entropy solutions. We define the class of strong generalized entropy solutions, in which the Cauchy problem has precisely one solution. We suggest a condition on the initial data under which any generalized entropy solution is strong, which implies its uniqueness. Under this condition we establish that the “vanishing viscosity” method converges. An example shows that in the general case there can be more than one generalized entropy solution.
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Izvestiya: Mathematics, 1999, 63:1, 129–179
MSC: 35K45, 35K55, 35L45, 35L65
E. Yu. Panov, “A non-local theory of generalized entropy solutions of the Cauchy problem for a class of hyperbolic systems of conservation laws”, Izv. RAN. Ser. Mat., 63:1 (1999), 133–184; Izv. Math., 63:1 (1999), 129–179
Citation in format AMSBIB
\paper A~non-local theory of generalized entropy solutions of the Cauchy problem for a~class of hyperbolic systems of conservation laws
\jour Izv. RAN. Ser. Mat.
\jour Izv. Math.
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This publication is cited in the following articles:
E. Yu. Panov, “On the theory of generalized entropy solutions of the Cauchy problem for a class of non-strictly hyperbolic systems of conservation laws”, Sb. Math., 191:1 (2000), 121–150
E. Yu. Panov, “On the symmetrizability of hyperbolic matrix spaces”, St. Petersburg Math. J., 20:3 (2009), 465–471
Panov, EY, “On infinite-dimensional Keyfitz-Kranzer systems of conservation laws”, Differential Equations, 45:2 (2009), 274
Crippa G., Spinolo L.V., “An Overview on Some Results Concerning the Transport Equation and its Applications To Conservation Laws”, Communications on Pure and Applied Analysis, 9:5 (2010), 1283–1293
N.H. Risebro, F. Weber, “A note on front tracking for the Keyfitz–Kranzer system”, Journal of Mathematical Analysis and Applications, 2013
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