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Volumn 17, Issue 4, 2000, Pages 413-472

Regularizing effects for multidimensional scalar conservation laws

Author keywords

Kinetic formulation of entropy solutions; Multidimensional scalar conservation laws; Radon transform; Scattering; Two microlocal regularity; Velocity averages

Indexed keywords


EID: 0012114154     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0294-1449(00)00116-5     Document Type: Article
Times cited : (15)

References (31)
  • 1
    • 0010922364 scopus 로고
    • Regularizing effects of homogeneous evolution equations
    • John Hopkins Univ. Press, Baltimore MD
    • 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.
    • (1981) Contributions to Analysis and Geometry , pp. 23-39
    • Bénilan, P.1    Crandall, M.G.2
  • 2
    • 22644449510 scopus 로고    scopus 로고
    • Averaging lemmas without time Fourier transform and applications to discretized kinetic equations
    • 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.
    • (1999) Proc. Royal Soc. Edinburgh A , vol.129 , pp. 19-36
    • Bouchut, F.1    Desvillettes, L.2
  • 4
    • 0021563988 scopus 로고
    • Averaged multivalued solutions fot scalar conservation laws
    • Brenier Y., Averaged multivalued solutions fot scalar conservation laws, SIAM J. Numer. Anal. 6 (1984) 1013-1037.
    • (1984) SIAM J. Numer. Anal. , vol.6 , pp. 1013-1037
    • Brenier, Y.1
  • 6
    • 0017426452 scopus 로고
    • The formation and decay of shocks for a conservation law in several dimensions
    • Conway E.D., The formation and decay of shocks for a conservation law in several dimensions, Arch. Rational Mech. Anal. 64 (1977) 47-57.
    • (1977) Arch. Rational Mech. Anal. , vol.64 , pp. 47-57
    • Conway, E.D.1
  • 7
    • 0005323179 scopus 로고
    • Asymptotic behavior of solutions of hyperbolic balance laws
    • Bardos C., Bessis D. (Eds.), Reidel, Dordrecht
    • 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.
    • (1979) Bifurcation Phenomena in Mathematical Physics , pp. 521-533
    • Dafermos, C.1
  • 8
    • 84971145260 scopus 로고
    • Regularity and large time behaviour of solutions of a conservation law without convexity
    • 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.
    • (1985) Proc. Roy. Soc. Edinburgh Sect. A , vol.99 , pp. 201-239
    • Dafermos, C.1
  • 10
    • 84987665752 scopus 로고
    • Large time behavior and homogenization of solutions of two-dimensional conservation laws
    • E W.
    • Engquist B., E W., Large time behavior and homogenization of solutions of two-dimensional conservation laws, Comm. Pure Apl. Math. 46 (1993) 1-26.
    • (1993) Comm. Pure Apl. Math. , vol.46 , pp. 1-26
    • Engquist, B.1
  • 11
    • 0003090940 scopus 로고
    • Moyennisation et régularité deux-microlocale
    • Gérard P., Moyennisation et régularité deux-microlocale, Ann. Sci. Ecole Norm. Sup. 23 (1990) 89-121.
    • (1990) Ann. Sci. Ecole Norm. Sup. , vol.23 , pp. 89-121
    • Gérard, P.1
  • 12
    • 45549114712 scopus 로고
    • Regularity of the moments of the solution of a transport equation
    • 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.
    • (1988) J. Funct. Anal. , vol.76 , pp. 110-125
    • Golse, F.1    Lions, P.L.2    Perthame, B.3    Sentis, R.4
  • 14
    • 0345990717 scopus 로고
    • First-order quasilinear equations in several independent variables
    • Kruzkov S.N., First-order quasilinear equations in several independent variables, Math. USSR-Sb. 64 (1977) 47-57.
    • (1977) Math. USSR-Sb. , vol.64 , pp. 47-57
    • Kruzkov, S.N.1
  • 15
    • 0003261490 scopus 로고
    • Hyperbolic systems of conservation laws and the mathematical theory of shock waves
    • SIAM
    • Lax P.D., Hyperbolic systems of conservation laws and the mathematical theory of shock waves, in: Regional Conference Series in Applied Mathematics, SIAM, 1973.
    • (1973) Regional Conference Series in Applied Mathematics
    • Lax, P.D.1
  • 16
    • 0001299964 scopus 로고
    • The formation and decay of shock waves
    • Lax P.D., The formation and decay of shock waves, Amer. Math. Month. 3 (1972) 227-241.
    • (1972) Amer. Math. Month. , vol.3 , pp. 227-241
    • Lax, P.D.1
  • 17
    • 0345990719 scopus 로고
    • Source solutions and asymptotic behavior in conservation laws
    • Liu T.P., Pierre M., Source solutions and asymptotic behavior in conservation laws, SIAM J. Math. Anal. 19 (1988) 763-773.
    • (1988) SIAM J. Math. Anal. , vol.19 , pp. 763-773
    • Liu, T.P.1    Pierre, M.2
  • 18
    • 84968518243 scopus 로고
    • A kinetic formulation of multidimensional scalar conservation laws and related equations
    • Lions PL., Perthame B., Tadmor E., A kinetic formulation of multidimensional scalar conservation laws and related equations, Bull. Amer. Math. Soc. 7 (1994) 169-189.
    • (1994) Bull. Amer. Math. Soc. , vol.7 , pp. 169-189
    • Lions, P.L.1    Perthame, B.2    Tadmor, E.3
  • 19
    • 0001105085 scopus 로고
    • Regularity through approximation for scalar conservation laws
    • Lucier B.J., Regularity through approximation for scalar conservation laws, Comm. Pure Appl. Math. 10 (1957) 537-566.
    • (1957) Comm. Pure Appl. Math. , vol.10 , pp. 537-566
    • Lucier, B.J.1
  • 20
    • 84973976230 scopus 로고
    • A Poincaré-Bendixon theorem for scalar balance laws
    • Lyberopoulos N., A Poincaré-Bendixon theorem for scalar balance laws, Proc. Royal Soc. Edinburgh A 124 (1994) 589-607.
    • (1994) Proc. Royal Soc. Edinburgh A , vol.124 , pp. 589-607
    • Lyberopoulos, N.1
  • 22
    • 0002717472 scopus 로고
    • Discontinuous solutions of nonlinear differential equations
    • Oleinik O., Discontinuous solutions of nonlinear differential equations, Usp. Mat. Nauk. 26 (1963) 95-172.
    • (1963) Usp. Mat. Nauk. , vol.26 , pp. 95-172
    • Oleinik, O.1
  • 23
    • 0032096818 scopus 로고    scopus 로고
    • A regularizing effect of nonlinear transport equations
    • F. Otto, A regularizing effect of nonlinear transport equations, Quart. Appl. Math. 56 (1998) 355-375.
    • (1998) Quart. Appl. Math. , vol.56 , pp. 355-375
    • Otto, F.1
  • 24
    • 0000741448 scopus 로고
    • A kinetic equation with kinetic entropy functions for scalar conservation laws
    • Perthame B., Tadmor E., A kinetic equation with kinetic entropy functions for scalar conservation laws, Comm. Math. Phys. 136 (1991) 501-517.
    • (1991) Comm. Math. Phys. , vol.136 , pp. 501-517
    • Perthame, B.1    Tadmor, E.2
  • 25
    • 0000075556 scopus 로고
    • A regularity theorem for conservation laws
    • Schaeffer D.G., A regularity theorem for conservation laws, Adv. in Math. 11 (1973) 368-386.
    • (1973) Adv. in Math. , vol.11 , pp. 368-386
    • Schaeffer, D.G.1
  • 27
    • 0005525132 scopus 로고
    • Une nouvelle méthode de résolution d'équations aux dérivées partielles non linéaires
    • Springer, Berlin
    • 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.
    • (1977) Lecture Notes in Math. , vol.665 , pp. 228-241
    • Tartar, L.1
  • 29
    • 0001168879 scopus 로고
    • The space BV and quasilinear equations
    • Volpert A.I., The space BV and quasilinear equations, Mat. Sb. 73 (1967). English translation: Math. USSR Sb. 2 (1967) 225-267.
    • (1967) Mat. Sb. , vol.73
    • Volpert, A.I.1
  • 30
    • 0001168879 scopus 로고
    • English translation
    • Volpert A.I., The space BV and quasilinear equations, Mat. Sb. 73 (1967). English translation: Math. USSR Sb. 2 (1967) 225-267.
    • (1967) Math. USSR Sb. , vol.2 , pp. 225-267
  • 31
    • 84990623109 scopus 로고
    • Decay rates for nonconvex systems of conservation laws
    • Zumbrun K., Decay rates for nonconvex systems of conservation laws, Comm. Pure Appl. Math. 46 (1993) 353-386.
    • (1993) Comm. Pure Appl. Math. , vol.46 , pp. 353-386
    • Zumbrun, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.