Regularizing effects for multidimensional scalar conservation laws
Cheverry, C.
Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000), p. 413-472 / Harvested from Numdam
Publié le : 2000-01-01
@article{AIHPC_2000__17_4_413_0,
     author = {Cheverry, Christophe},
     title = {Regularizing effects for multidimensional scalar conservation laws},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {17},
     year = {2000},
     pages = {413-472},
     mrnumber = {1782740},
     zbl = {0966.35074},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2000__17_4_413_0}
}
Cheverry, C. Regularizing effects for multidimensional scalar conservation laws. Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) pp. 413-472. http://gdmltest.u-ga.fr/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 648452 | Zbl 0556.35067

[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 1669221 | Zbl 0933.35159

[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 765504 | Zbl 0565.65054

[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 1721342 | Zbl 1069.35509

[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 427850 | Zbl 0352.35029

[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 580309 | Zbl 0464.35060

[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 785530 | Zbl 0616.35054

[9] Diperna R.J., Lions P.L., Meyer Y., Lp regularity of velocity averages, Ann. Inst. Henri Poincaré 8 (1991) 271-287. | Numdam | MR 1127927 | Zbl 0763.35014

[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 1193341 | Zbl 0797.35114

[11] Gérard P., Moyennisation et régularité deux-microlocale, Ann. Sci. Ecole Norm. Sup. 23 (1990) 89-121. | Numdam | MR 1042388 | Zbl 0725.35003

[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 923047 | Zbl 0652.47031

[13] Helgason S., The Radon Transform, Progress in Mathematics, Vol. 5, Birkhäuser. | MR 1723736 | Zbl 0453.43011

[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 350216 | Zbl 0268.35062

[16] Lax P.D., The formation and decay of shock waves, Amer. Math. Month. 3 (1972) 227-241. | MR 298252 | Zbl 0228.35019

[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 1201239 | Zbl 0820.35094

[19] Lucier B.J., Regularity through approximation for scalar conservation laws, Comm. Pure Appl. Math. 10 (1957) 537-566. | MR 946641

[20] Lyberopoulos N., A Poincaré-Bendixon theorem for scalar balance laws, Proc. Royal Soc. Edinburgh A 124 (1994) 589-607. | MR 1286920 | Zbl 0806.35111

[21] Murat F., Compacité par compensation, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 5 (1978) 489-507. | Numdam | MR 506997 | Zbl 0399.46022

[22] Oleinik O., Discontinuous solutions of nonlinear differential equations, Usp. Mat. Nauk. 26 (1963) 95-172. | Zbl 0131.31803

[23] F Otto, A regularizing effect of nonlinear transport equations, Quart. Appl. Math. 56 ( 1998) 355-375. | MR 1622511 | Zbl 0970.35115

[24] Perthame B., Tadmor E., A kinetic equation with kinetic entropy functions for scalar conservation laws, Comm. Math. Phys. 136 (1991) 501-517. | MR 1099693 | Zbl 0729.76070

[25] Schaeffer D.G., A regularity theorem for conservation laws, Adv. in Math. 11 (1973) 368-386. | MR 326178 | Zbl 0267.35009

[26] Serre D., Systèmes de lois de conservation I, Diderot éditeur, arts et sciences. | MR 1459988

[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 519433 | Zbl 0414.35068

[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 216338 | Zbl 0168.07402

[30] Zumbrun K., Decay rates for nonconvex systems of conservation laws, Comm. Pure Appl. Math. 46 (1993) 353-386. | MR 1202961 | Zbl 0799.35154