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Volumn 32, Issue 7, 1998, Pages 891-933

One-dimensional transport equations with discontinuous coefficients

Author keywords

Discontinuous coefficients; Duality; Linear transport equations; Nonnegative solutions; Product of a measure by a discontinuous function; Weak stability

Indexed keywords

FUNCTIONS; PROBLEM SOLVING;

EID: 0032092187     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00536-1     Document Type: Article
Times cited : (212)

References (26)
  • 3
    • 0002178812 scopus 로고
    • Delta-shock waves as limits of vanishing viscosity for hyperbolic systems of conservation laws
    • Tan, D., Zhang, T. and Zheng, Y., Delta-shock waves as limits of vanishing viscosity for hyperbolic systems of conservation laws. J. Diff. Eq., 1994, 112, 1-32.
    • (1994) J. Diff. Eq. , vol.112 , pp. 1-32
    • Tan, D.1    Zhang, T.2    Zheng, Y.3
  • 4
    • 84990610649 scopus 로고
    • Existence of global weak solutions to one-component Vlasov-Poisson and Fokker-Planck-Poisson systems in one space dimension with measures as initial data
    • Zheng, Y. and Majda, A., Existence of global weak solutions to one-component Vlasov-Poisson and Fokker-Planck-Poisson systems in one space dimension with measures as initial data. Comm. on Pure and Appl. Math., 1994, 47, 1365-1401.
    • (1994) Comm. on Pure and Appl. Math. , vol.47 , pp. 1365-1401
    • Zheng, Y.1    Majda, A.2
  • 6
    • 0000584073 scopus 로고
    • Existence globale pour le système des gaz sans pression
    • Serie I
    • Grenier, E., Existence globale pour le système des gaz sans pression. C.R. Acad. Sci. Paris, 1995, 321, Serie I, 171-174.
    • (1995) C.R. Acad. Sci. Paris , vol.321 , pp. 171-174
    • Grenier, E.1
  • 7
    • 0040823847 scopus 로고
    • On the model of pressureless gases with sticky particles
    • Report No. 94-45
    • Brenier, Y. and Grenier, E., On the model of pressureless gases with sticky particles. UCLA Computational and Applied Math., Report No. 94-45, 1994.
    • (1994) UCLA Computational and Applied Math.
    • Brenier, Y.1    Grenier, E.2
  • 8
    • 0001766126 scopus 로고    scopus 로고
    • Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics
    • E, W.
    • E, W., Rykov, Y. G. and Sinai, Y. G., Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics. Comm. Math. Phys., 1996, 177, 349-380.
    • (1996) Comm. Math. Phys. , vol.177 , pp. 349-380
    • Rykov, Y.G.1    Sinai, Y.G.2
  • 10
    • 0002306354 scopus 로고
    • Ordinary differential equations, transport theory and Sobolev spaces
    • DiPerna, R. J. and Lions, P. L., Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math., 1989, 98, 511-547.
    • (1989) Invent. Math. , vol.98 , pp. 511-547
    • DiPerna, R.J.1    Lions, P.L.2
  • 11
    • 0000563828 scopus 로고    scopus 로고
    • On some analogy between different approaches to first order PDE's with nonsmooth coefficients
    • Capuzzo Dolcetta, I. and Perthame, B., On some analogy between different approaches to first order PDE's with nonsmooth coefficients. Advances in Math. Sci. and Appl., 1996, 6, 689-703.
    • (1996) Advances in Math. Sci. and Appl. , vol.6 , pp. 689-703
    • Capuzzo Dolcetta, I.1    Perthame, B.2
  • 12
    • 0001522672 scopus 로고
    • Definition and weak stability of nonconservative products
    • Dal Maso, G., Le Floch, P. and Murat, F., Definition and weak stability of nonconservative products. J. Math. Pures Appl., 1995, 74, 483-548.
    • (1995) J. Math. Pures Appl. , vol.74 , pp. 483-548
    • Dal Maso, G.1    Le Floch, P.2    Murat, F.3
  • 13
    • 0002717472 scopus 로고
    • Discontinuous solutions of nonlinear differential equations
    • Oleinik, O. A., Discontinuous solutions of nonlinear differential equations. Amer. Math. Soc. Transl., 1963, 26(2), 95-172.
    • (1963) Amer. Math. Soc. Transl. , vol.26 , Issue.2 , pp. 95-172
    • Oleinik, O.A.1
  • 14
    • 0000446066 scopus 로고
    • Generalized solutions of linear differential equations with discontinuous coefficients and the uniqueness question for multidimensional quasilinear conservation laws
    • Conway, E. D., Generalized solutions of linear differential equations with discontinuous coefficients and the uniqueness question for multidimensional quasilinear conservation laws. J. of Math. Anal. and Appl., 1967, 18, 238-251.
    • (1967) J. of Math. Anal. and Appl. , vol.18 , pp. 238-251
    • Conway, E.D.1
  • 15
    • 84967790444 scopus 로고
    • The Sharp form of Oleinik's entropy condition in several space variables
    • Hoff, D., The Sharp form of Oleinik's entropy condition in several space variables. Trans. of the A.M.S., 1983, 276, 707-714.
    • (1983) Trans. of the A.M.S. , vol.276 , pp. 707-714
    • Hoff, D.1
  • 16
    • 0026203648 scopus 로고
    • Local error estimates for discontinuous solutions of nonlinear hyperbolic equations
    • Tadmor, E., Local error estimates for discontinuous solutions of nonlinear hyperbolic equations. SIAM J. Numer. Anal., 1991, 28, 891-906.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 891-906
    • Tadmor, E.1
  • 17
    • 84990557326 scopus 로고
    • Uniqueness via the adjoint problems for systems of conservation laws
    • Le Floch, P. and Xin, Z., Uniqueness via the adjoint problems for systems of conservation laws. Comm. on Pure and Applied Maths., 1993, XLVI(11), 1499-1533.
    • (1993) Comm. on Pure and Applied Maths. , vol.46 , Issue.11 , pp. 1499-1533
    • Le Floch, P.1    Xin, Z.2
  • 18
    • 0002299782 scopus 로고
    • Differential equations with discontinuous righthand side
    • Filippov, A. F., Differential equations with discontinuous righthand side. A.M.S. Transl., 1964, 42(2), 199-231.
    • (1964) A.M.S. Transl. , vol.42 , Issue.2 , pp. 199-231
    • Filippov, A.F.1
  • 20
    • 84983423812 scopus 로고
    • Differential equations with discontinuous righthand sides
    • Kluwer Academic Publishers, Dordrecht
    • Filippov, A. F., Differential equations with discontinuous righthand sides. Coll. Mathematics and Its Applications. Kluwer Academic Publishers, Dordrecht, 1988.
    • (1988) Coll. Mathematics and Its Applications
    • Filippov, A.F.1
  • 21
    • 0000617788 scopus 로고
    • Generalized characteristics and the structure of solutions of hyperabolic conservation laws
    • Dafermos, C. M., Generalized characteristics and the structure of solutions of hyperabolic conservation laws. Indiana Univ. Math. J., 1977, 26, 1097-1119.
    • (1977) Indiana Univ. Math. J. , vol.26 , pp. 1097-1119
    • Dafermos, C.M.1
  • 22
    • 0001400260 scopus 로고
    • On the piecewise smoothness of entropy solutions to scalar conservation laws
    • Tadmor, E. and Tassa, T., On the piecewise smoothness of entropy solutions to scalar conservation laws. Comm. in P.D.E., 1993, 18, 1631-1652.
    • (1993) Comm. in P.D.E. , vol.18 , pp. 1631-1652
    • Tadmor, E.1    Tassa, T.2
  • 23
    • 0001521650 scopus 로고
    • Equations de transport unidimensionnelles à coefficients discontinus
    • Serie I
    • Bouchut, F. and James, F., Equations de transport unidimensionnelles à coefficients discontinus. C.R. Acad. Sci. Paris, 1995, 320, Serie I, 1097-1102.
    • (1995) C.R. Acad. Sci. Paris , vol.320 , pp. 1097-1102
    • Bouchut, F.1    James, F.2
  • 24
    • 0000534665 scopus 로고
    • Source-solutions and asymptotic behavior in conservation laws
    • Liu, T.-P. and Pierre, M., Source-solutions and asymptotic behavior in conservation laws. J. Diff. Eq., 1984, 51, 419-441.
    • (1984) J. Diff. Eq. , vol.51 , pp. 419-441
    • Liu, T.-P.1    Pierre, M.2
  • 26
    • 85033910814 scopus 로고
    • Thesis Université Paris 6
    • Serfati, P., Thesis Université Paris 6, 1992.
    • (1992)
    • Serfati, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.