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Volumn 159, Issue 2, 1999, Pages 447-484

Riemann problems for a class of coupled hyperbolic systems of conservation laws

Author keywords

Coupled hyperbolic system; Delta shock waves; Entropy condition; Generalized Rankine Hugoniot relation; Measure solution

Indexed keywords


EID: 0033544732     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1999.3629     Document Type: Article
Times cited : (149)

References (25)
  • 2
    • 0001230725 scopus 로고
    • On zero-pressure gas dynamics
    • Series on Advances in Mathematics for Applied Sciences. Singapore: World Scientific. p. 171-190
    • Bouchut F. On zero-pressure gas dynamics. Advances in Kinetic Theory and Computing. Series on Advances in Mathematics for Applied Sciences. 22:1994;World Scientific, Singapore. p. 171-190.
    • (1994) Advances in Kinetic Theory and Computing , vol.22
    • Bouchut, F.1
  • 4
    • 0030147154 scopus 로고    scopus 로고
    • Existence and asymptotic behavior of measure-valued solutions for degenerate conservation laws
    • Chen G. Q., Frid H. Existence and asymptotic behavior of measure-valued solutions for degenerate conservation laws. J. Differential Equations. 127:1996;197-224.
    • (1996) J. Differential Equations , vol.127 , pp. 197-224
    • Chen G., Q.1    Frid, H.2
  • 5
    • 0003835038 scopus 로고
    • The Riemann problem and interaction of waves in gas dynamics
    • Essex: Longman
    • Chang T., Hsiao L. The Riemann problem and interaction of waves in gas dynamics. Pitman Monographs. 1989;Longman, Essex.
    • (1989) Pitman Monographs
    • Chang, T.1    Hsiao, L.2
  • 6
    • 0015746230 scopus 로고
    • Solution of the Riemann problem for a class of hyperbolic systems of conservation laws by viscosity method
    • Dafermos C. M. Solution of the Riemann problem for a class of hyperbolic systems of conservation laws by viscosity method. Arch. Rational Mech. Anal. 52:1973;1-9.
    • (1973) Arch. Rational Mech. Anal. , vol.52 , pp. 1-9
    • Dafermos C., M.1
  • 7
    • 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
    • Weinan E., Rykov Yu. G., Sinai Ya. 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. 177:1996;349-380.
    • (1996) Comm. Math. Phys. , vol.177 , pp. 349-380
    • Weinan, E.1    Rykov Yu., G.2    Sinai Ya., G.3
  • 8
    • 0009264168 scopus 로고
    • Multivalued solutions to some nonlinear and nonstrictly hyperbolic systems
    • Forester A., Le Floch P. Multivalued solutions to some nonlinear and nonstrictly hyperbolic systems. Japan J. Indust. Appl. Math. 9:1992;1-23.
    • (1992) Japan J. Indust. Appl. Math. , vol.9 , pp. 1-23
    • Forester, A.1    Le Floch, P.2
  • 9
    • 0000088106 scopus 로고
    • Some problem in the theory of quasilinear equations
    • Gelfand I. Some problem in the theory of quasilinear equations. Uspekhi Mat. Nauk. 14:1959;87-158.
    • (1959) Uspekhi Mat. Nauk , vol.14 , pp. 87-158
    • Gelfand, I.1
  • 11
    • 0027607979 scopus 로고
    • A Riemann problem whose viscosity solutions contain delta-measures
    • Joseph K. T. A Riemann problem whose viscosity solutions contain delta-measures. Asymptotic Anal. 7:1993;105-120.
    • (1993) Asymptotic Anal. , vol.7 , pp. 105-120
    • Joseph K., T.1
  • 14
    • 0003222778 scopus 로고
    • An existence and uniqueness result for two nonstrictly hyperbolic systems
    • IMA Math. Appl. New York/Berlin: Springer-Verlag
    • Le Floch P. An existence and uniqueness result for two nonstrictly hyperbolic systems. Nonlinear Evolution Equations That Change Type. IMA Math. Appl. 27:1990;Springer-Verlag, New York/Berlin.
    • (1990) Nonlinear Evolution Equations That Change Type , vol.27
    • Le Floch, P.1
  • 15
    • 0003343266 scopus 로고
    • Nonlinear stability of shock waves for viscous conservation laws
    • Liu T. P. Nonlinear stability of shock waves for viscous conservation laws. Mem. Amer. Math. Soc. 328:1986.
    • (1986) Mem. Amer. Math. Soc. , vol.328
    • Liu T., P.1
  • 16
    • 0009109756 scopus 로고    scopus 로고
    • Generalized Rankine-Hugoniot relations of delta-shocks in solutions of transportation equations
    • G. Q. Chen. Singapore: World Scientific
    • Li J., Zhang T. Generalized Rankine-Hugoniot relations of delta-shocks in solutions of transportation equations. Chen G. Q., Nonlinear PDE and Related Areas. 1998;219-232 World Scientific, Singapore.
    • (1998) Nonlinear PDE and Related Areas , pp. 219-232
    • Li, J.1    Zhang, T.2
  • 18
    • 84966229350 scopus 로고
    • Riemann problems for nonstrictly hyperbolic 2×2 systems of conservation laws
    • Schaeffer D., Shearer M. Riemann problems for nonstrictly hyperbolic 2×2 systems of conservation laws. Trans. Amer. Math. Soc. 304:1987;267-306.
    • (1987) Trans. Amer. Math. Soc. , vol.304 , pp. 267-306
    • Schaeffer, D.1    Shearer, M.2
  • 19
    • 0032623122 scopus 로고    scopus 로고
    • The Riemann problem for transportation equations in gas dynamics
    • Sheng W., Zhang T. The Riemann problem for transportation equations in gas dynamics. Mem. Amer. Math. Soc. 137:1999.
    • (1999) Mem. Amer. Math. Soc. , vol.137
    • Sheng, W.1    Zhang, T.2
  • 20
    • 43949161016 scopus 로고
    • Two-dimensional Riemann problem for a hyperbolic system of nonlinear conservation laws. I. Four-J cases
    • Tan D., Zhang T. Two-dimensional Riemann problem for a hyperbolic system of nonlinear conservation laws. I. Four-J cases. J. Differential Equations. 111:1994;203-254.
    • (1994) J. Differential Equations , vol.111 , pp. 203-254
    • Tan, D.1    Zhang, T.2
  • 21
    • 0002178812 scopus 로고
    • Delta-shock waves as limits of vanishing viscosity for hyperbolic system of conservation laws
    • Tan D., Zhang T., Zheng Y. Delta-shock waves as limits of vanishing viscosity for hyperbolic system of conservation laws. J. Differential Equations. 112:1994;1-32.
    • (1994) J. Differential Equations , vol.112 , pp. 1-32
    • Tan, D.1    Zhang, T.2    Zheng, Y.3
  • 23
    • 85031454285 scopus 로고    scopus 로고
    • Delta-shocks as limits of vanishing viscosity for multidimensional zero-pressure gas dynamics
    • in press
    • H. Yang, and J. Li, Delta-shocks as limits of vanishing viscosity for multidimensional zero-pressure gas dynamics, Quarterly Appl. Math., in press.
    • Quarterly Appl. Math.
    • Yang, H.1    Li, J.2
  • 25
    • 0000329914 scopus 로고
    • Conjecture on the structure of solution of the Riemann problem of two-dimensional gas dynamics systems
    • Zhang T., Zheng Y. Conjecture on the structure of solution of the Riemann problem of two-dimensional gas dynamics systems. SIAM J. Math. Anal. 21:1990;593-625.
    • (1990) SIAM J. Math. Anal. , vol.21 , pp. 593-625
    • Zhang, T.1    Zheng, Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.