Regularizing effects for multidimensional scalar conservation laws
Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) no. 4, pp. 413-472. 
@article{AIHPC_2000__17_4_413_0,
     author = {Cheverry, C.},
     title = {Regularizing effects for multidimensional scalar conservation laws},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {413--472},
     publisher = {Gauthier-Villars},
     volume = {17},
     number = {4},
     year = {2000},
     mrnumber = {1782740},
     zbl = {0966.35074},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_2000__17_4_413_0/}
}
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Cheverry, C. Regularizing effects for multidimensional scalar conservation laws. Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) no. 4, pp. 413-472. http://archive.numdam.org/item/AIHPC_2000__17_4_413_0/

[1] Bénilan P., Crandall M.G., Regularizing effects of homogeneous evolution equations, in: Contributions to Analysis and Geometry, John Hopkins Univ. Press, Baltimore MD, 1981, pp. 23-39. | MR | Zbl

[2] Bouchut F., Desvillettes L., Averaging lemmas without time Fourier transform and applications to discretized kinetic equations, Proc. Royal Soc. Edinburgh A 129 (1999) 19-36. | MR | Zbl

[3] Bouchut F., Introduction to the mathematical theory of kinetic equations, in: Coll. Series in Appl. Math. Session "L'état de la recherche" de la S. M. F., Equations cinétiques, Orléans, Elsevier, Amsterdam, 1998.

[4] Brenier Y., Averaged multivalued solutions fot scalar conservation laws, SIAM J. Numer. Anal. 6 (1984) 1013-1037. | MR | Zbl

[5] Cheverry C., Effet régularisant pour une loi de conservation scalaire multidimensionnelle, Séminaire: Equations aux derivees partielles, 1998-99, Exp. No. XXIV, 15 pp., Ecole Polytechnique, Palaiseau. | Numdam | MR | Zbl

[6] Conway E.D., The formation and decay of shocks for a conservation law in several dimensions, Arch. Rational Mech. Anal. 64 (1977) 47-57. | MR | Zbl

[7] Dafermos C., Asymptotic behavior of solutions of hyperbolic balance laws, in: Bardos C., Bessis D. (Eds.), Bifurcation Phenomena in Mathematical Physics, Reidel, Dordrecht, 1979, pp. 521-533. | MR | Zbl

[8] Dafermos C., Regularity and large time behaviour of solutions of a conservation law without convexity, Proc. Roy. Soc. Edinburgh Sect. A 99 (1985) 201-239. | MR | Zbl

[9] Diperna R.J., Lions P.L., Meyer Y., Lp regularity of velocity averages, Ann. Inst. Henri Poincaré 8 (1991) 271-287. | Numdam | MR | Zbl

[10] Engquist B.E.W., Large time behavior and homogenization of solutions of two-dimensional conservation laws, Comm. Pure Apl. Math. 46 (1993) 1-26. | MR | Zbl

[11] Gérard P., Moyennisation et régularité deux-microlocale, Ann. Sci. Ecole Norm. Sup. 23 (1990) 89-121. | Numdam | MR | Zbl

[12] Golse F., Lions P.L., Perthame B., Sentis R., Regularity of the moments of the solution of a transport equation, J. Funct. Anal. 76 (1988) 110-125. | MR | Zbl

[13] Helgason S., The Radon Transform, Progress in Mathematics, Vol. 5, Birkhäuser. | MR | Zbl

[14] Kruzkov S.N., First-order quasilinear equations in several independent variables, Math. USSR-Sb. 64 (1977) 47-57.

[15] Lax P.D., Hyperbolic systems of conservation laws and the mathematical theory of shock waves, in: Regional Conference Series in Applied Mathematics, SIAM, 1973. | MR | Zbl

[16] Lax P.D., The formation and decay of shock waves, Amer. Math. Month. 3 (1972) 227-241. | MR | Zbl

[17] Liu T.P., Pierre M., Source solutions and asymptotic behavior in conservation laws, SIAM J. Math. Anal. 19 (1988) 763-773.

[18] Lions P.L., Perthame B., Tadmor E., A kinetic formulation of multidimensional scalar conservation laws and related equations, Bull. Amer. Math. Soc. 7 (1994) 169-189. | MR | Zbl

[19] Lucier B.J., Regularity through approximation for scalar conservation laws, Comm. Pure Appl. Math. 10 (1957) 537-566. | MR

[20] Lyberopoulos N., A Poincaré-Bendixon theorem for scalar balance laws, Proc. Royal Soc. Edinburgh A 124 (1994) 589-607. | MR | Zbl

[21] Murat F., Compacité par compensation, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 5 (1978) 489-507. | Numdam | MR | Zbl

[22] Oleinik O., Discontinuous solutions of nonlinear differential equations, Usp. Mat. Nauk. 26 (1963) 95-172. | Zbl

[23] F Otto, A regularizing effect of nonlinear transport equations, Quart. Appl. Math. 56 ( 1998) 355-375. | MR | Zbl

[24] Perthame B., Tadmor E., A kinetic equation with kinetic entropy functions for scalar conservation laws, Comm. Math. Phys. 136 (1991) 501-517. | MR | Zbl

[25] Schaeffer D.G., A regularity theorem for conservation laws, Adv. in Math. 11 (1973) 368-386. | MR | Zbl

[26] Serre D., Systèmes de lois de conservation I, Diderot éditeur, arts et sciences. | MR

[27] Tartar L., Une nouvelle méthode de résolution d'équations aux dérivées partielles non linéaires, in: Lecture Notes in Math., Vol. 665, Springer, Berlin, 1977, pp. 228- 241. | MR | Zbl

[28] Vasseur A., Contributions à l'approche cinétique des systèmes de lois de conservation hyperboliques, Thèse de doctorat de l'université Paris 6, 1999.

[29] Volpert A.I., The space BV and quasilinear equations, Mat. Sb. 73 (1967). English translation: Math. USSR Sb. 2 (1967) 225-267. | MR | Zbl

[30] Zumbrun K., Decay rates for nonconvex systems of conservation laws, Comm. Pure Appl. Math. 46 (1993) 353-386. | MR | Zbl