Geodesic
Renormalized entropy solutions of the Cauchy problem for a first-order inhomogeneous quasilinear equation
Sbornik. Mathematics, Tome 204 (2013) no. 10, pp. 1480-1515 Cet article a éte moissonné depuis la source Math-Net.Ru

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The concept of a renormalized entropy solution of the Cauchy problem for an inhomogeneous quasilinear equation of the first order is introduced. Existence and uniqueness theorems are proved, together with a comparison principle. Connections with generalized entropy solutions are investigated. Bibliography: 10 titles.
Keywords: first-order quasilinear equations, generalized entropy solutions, comparison principle, renormalized solutions, existence and uniqueness. 
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E. Yu. Panov. Renormalized entropy solutions of the Cauchy problem for a first-order inhomogeneous quasilinear equation. Sbornik. Mathematics, Tome 204 (2013) no. 10, pp. 1480-1515. http://geodesic.mathdoc.fr/item/SM_2013_204_10_a2/

[1] S. N. Kružkov, “First order quasilinear equations in several independent variables”, Math. USSR-Sb., 10:2 (1970), 217–243 | DOI | MR | Zbl | Zbl

[2] E. Yu. Panov, “On generalized entropy solutions of the Cauchy problem for a first-order quasilinear equation in the class of locally summable functions”, Izv. Math., 66:6 (2002), 1171–1218 | DOI | DOI | MR | Zbl

[3] Ph. Bénilan, S.N. Kruzhkov, “Conservation laws with continuous flux functions”, NoDEA Nonlinear Differential Equations Appl., 3:4 (1996), 395–419 | DOI | MR | Zbl

[4] S. N. Kruzhkov, E. Yu. Panov, “Osgood's type conditions for uniqueness of entropy solutions to Cauchy problem for quasilinear conservation laws of the first order”, Ann. Univ. Ferrara Sez. VII (N.S.), 40 (1994), 31–54 | MR | Zbl

[5] A. Yu. Goritsky, E. Yu. Panov, “Example of nonuniqueness of entropy solutions in the class of locally bounded functions”, Russ. J. Math. Phys., 6:4 (1999), 492–494 | MR | Zbl

[6] A. Yu. Goritsky, E. Yu. Panov, “Locally bounded generalized entropy solutions to the Cauchy problem for a first-order quasilinear equation”, Proc. Steklov Inst. Math., 236 (2002), 110–123 | MR | Zbl

[7] E. Yu. Panov, “On well-posedness classes of locally bounded generalized entropy solutions of the Cauchy problem for quasilinear first-order equations”, J. Math. Sci., 150:6 (2008), 2578–2587 | DOI | MR | Zbl

[8] Ph. Bénilan, J. Carrillo, P. Wittbold, “Renormalized entropy solutions of scalar conservation laws”, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 29:2 (2000), 313–327 | MR | Zbl

[9] P. V. Lysukho, E. Yu. Panov, “Renormalizovannye entropiinye resheniya zadachi Koshi dlya kvazilineinogo uravneniya pervogo poryadka”, Prob. matem. analiza, 51, 2010, 3–20

[10] O. A. Oleinik, “Razryvnye resheniya nelineinykh differentsialnykh uravnenii”, UMN, 12:3(75) (1957), 3–73 | MR | Zbl