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Volumn 39, Issue 4, 2002, Pages 1197-1218

A difference scheme for conservation laws with a discontinuous flux: The nonconvex case

Author keywords

Conservation laws; Difference approximations; Discontinuous coefficients; Nonconvex; Source terms

Indexed keywords


EID: 0035453016     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142900374974     Document Type: Article
Times cited : (96)

References (22)
  • 1
    • 84966217981 scopus 로고
    • Monotone difference approximations for scalar conservation laws
    • M.G. CRANDALL AND A. MAJDA, Monotone difference approximations for scalar conservation laws, Math. Comp., 34 (1980), pp. 1-21.
    • (1980) Math. Comp. , vol.34 , pp. 1-21
    • Crandall, M.G.1    Majda, A.2
  • 2
    • 84966243152 scopus 로고
    • Some relations between nonexpansive and order preserving mappings
    • M.G. CRANDALL AND L. TARTAR, Some relations between nonexpansive and order preserving mappings, Proc. Amer. Math. Soc., 78 (1980), pp. 385-390.
    • (1980) Proc. Amer. Math. Soc. , vol.78 , pp. 385-390
    • Crandall, M.G.1    Tartar, L.2
  • 3
    • 84966208277 scopus 로고
    • One-sided difference approximations for nonlinear conservation laws
    • B. ENGQUIST AND S. OSHER, One-sided difference approximations for nonlinear conservation laws, Math. Comp., 36 (1981), pp. 321-351.
    • (1981) Math. Comp. , vol.36 , pp. 321-351
    • Engquist, B.1    Osher, S.2
  • 4
    • 0001087875 scopus 로고    scopus 로고
    • Analysis and approximation of conservation laws with source terms
    • J.M. GREENBERG, A.Y. LEROUX, R. BARAILLE, AND A. NOUSSAIR, Analysis and approximation of conservation laws with source terms, SIAM J. Numer. Anal., 34 (1997), pp. 1980-2007.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 1980-2007
    • Greenberg, J.M.1    Leroux, A.Y.2    Baraille, R.3    Noussair, A.4
  • 5
    • 40749159424 scopus 로고
    • High resolution schmes for hyperbolic conservation laws
    • A. HARTEN, High resolution schmes for hyperbolic conservation laws, J. Comput. Phys., 49 (1983), pp. 357-393.
    • (1983) J. Comput. Phys. , vol.49 , pp. 357-393
    • Harten, A.1
  • 6
    • 84980170156 scopus 로고
    • On finite difference approximations and entropy conditions for shocks
    • A. HARTEN, J.M. HYMAN, AND P.D. LAX, On finite difference approximations and entropy conditions for shocks, Comm. Pure Appl. Math., 29 (1976), pp. 297-322.
    • (1976) Comm. Pure Appl. Math. , vol.29 , pp. 297-322
    • Harten, A.1    Hyman, J.M.2    Lax, P.D.3
  • 8
    • 0033196472 scopus 로고    scopus 로고
    • Stability of conservation laws with discontinuous coefficients
    • R.A. KLAUSEN AND N.H. RISEBRO, Stability of conservation laws with discontinuous coefficients, J. Differential Equations, 157 (1999), pp. 41-60.
    • (1999) J. Differential Equations , vol.157 , pp. 41-60
    • Klausen, R.A.1    Risebro, N.H.2
  • 9
    • 0000055941 scopus 로고
    • Convex conservation laws with discontinuous coefficients. Existence, uniqueness, and asymptotic behavior
    • C. KLINGENBERG AND N.H. RISEBRO, Convex conservation laws with discontinuous coefficients. Existence, uniqueness, and asymptotic behavior, Comm. Partial Differential Equations, 20 (1995), pp. 1959-1990.
    • (1995) Comm. Partial Differential Equations , vol.20 , pp. 1959-1990
    • Klingenberg, C.1    Risebro, N.H.2
  • 10
    • 0035285314 scopus 로고    scopus 로고
    • Stability of a resonant system of conservation laws modeling polymer flow with gravitation
    • C. KLINGENBERG AND N.H. RISEBRO, Stability of a resonant system of conservation laws modeling polymer flow with gravitation, J. Differential Equations, 170 (2001), pp. 344-380.
    • (2001) J. Differential Equations , vol.170 , pp. 344-380
    • Klingenberg, C.1    Risebro, N.H.2
  • 12
    • 0001279338 scopus 로고
    • A comparison of convergence rates for Godunov's method and Glimm's method in resonant nonlinear systems of conservation laws
    • L. LIN, J.B. TEMPLE, AND J. WANG, A comparison of convergence rates for Godunov's method and Glimm's method in resonant nonlinear systems of conservation laws, SIAM J. Numer. Anal., 32 (1995), pp. 824-840.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 824-840
    • Lin, L.1    Temple, J.B.2    Wang, J.3
  • 13
    • 0000730728 scopus 로고
    • Suppression of oscillations in Godunov's method for a resonant non-strictly hyperbolic system
    • L. LONGWEI, J.B. TEMPLE, AND W. JINGHUA, Suppression of oscillations in Godunov's method for a resonant non-strictly hyperbolic system, SIAM J. Numer. Anal., 32 (1995), pp. 841-864.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 841-864
    • Longwei, L.1    Temple, J.B.2    Jinghua, W.3
  • 14
    • 0033328873 scopus 로고    scopus 로고
    • Viscosity solutions and convergence of monotone schemes for synthetic aperture radar shape-from-shading equations with discontinuous intensities
    • D.N. OSTROV, Viscosity solutions and convergence of monotone schemes for synthetic aperture radar shape-from-shading equations with discontinuous intensities, SIAM J. Appl. Math., 59 (1999), pp. 2060-2085.
    • (1999) SIAM J. Appl. Math. , vol.59 , pp. 2060-2085
    • Ostrov, D.N.1
  • 15
    • 0041539914 scopus 로고    scopus 로고
    • Solutions of Hamilton-Jacobi equations and scalar conservation laws with discontinuous space-time dependence
    • to appear
    • D.N. OSTROV, Solutions of Hamilton-Jacobi equations and scalar conservation laws with discontinuous space-time dependence, J. Differential Equations, to appear.
    • J. Differential Equations
    • Ostrov, D.N.1
  • 16
    • 84966203226 scopus 로고
    • On convergence of monotone difference schemes with variable spatial differencing
    • R. SANDERS, On convergence of monotone difference schemes with variable spatial differencing, Math. Comp., 40 (1983), pp. 91-106.
    • (1983) Math. Comp. , vol.40 , pp. 91-106
    • Sanders, R.1
  • 18
    • 49049142492 scopus 로고
    • Global solution of the Cauchy problem for a class of 2 × 2 nonstrictly hyperbolic conservation laws
    • B. TEMPLE, Global solution of the Cauchy problem for a class of 2 × 2 nonstrictly hyperbolic conservation laws, Adv. Appl. Math., 3 (1982), pp. 335-375.
    • (1982) Adv. Appl. Math. , vol.3 , pp. 335-375
    • Temple, B.1
  • 19
    • 0034449655 scopus 로고    scopus 로고
    • Convergence of a difference scheme for conservation laws with a discontinuous flux
    • J.D. TOWERS, Convergence of a difference scheme for conservation laws with a discontinuous flux, SIAM J. Numer. Anal., 38 (2000), pp. 681-698.
    • (2000) SIAM J. Numer. Anal. , vol.38 , pp. 681-698
    • Towers, J.D.1
  • 21
    • 0000814788 scopus 로고
    • The solution of nonstrictly hyperbolic conservation laws may be hard to compute
    • A. TVEITO AND R. WINTHER, The solution of nonstrictly hyperbolic conservation laws may be hard to compute, SIAM J. Sci. Comput., 16 (1995), pp. 320-329.
    • (1995) SIAM J. Sci. Comput. , vol.16 , pp. 320-329
    • Tveito, A.1    Winther, R.2
  • 22
    • 0000550068 scopus 로고    scopus 로고
    • The immersed interface method for nonlinear differential equations with discontinuous coefficients and singular sources
    • A. WIEGMANN AND K.P. BUBE, The immersed interface method for nonlinear differential equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal., 35 (1998), pp. 177-200.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 177-200
    • Wiegmann, A.1    Bube, K.P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.