메뉴 건너뛰기




Volumn 161, Issue 1, 2005, Pages 223-342

Vanishing viscosity solutions of nonlinear hyperbolic systems

Author keywords

[No Author keywords available]

Indexed keywords


EID: 23744450066     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.4007/annals.2005.161.223     Document Type: Article
Times cited : (397)

References (52)
  • 1
    • 2142824143 scopus 로고    scopus 로고
    • Well posedness for general 2 × 2 systems of conservation laws
    • [AM]
    • [AM] F. ANCONA and A. MARSON, Well Posedness for General 2 × 2 Systems of Conservation Laws, Mem. Amer. Math. Soc. 801 (2001).
    • (2001) Mem. Amer. Math. Soc. , vol.801
    • Ancona, F.1    Marson, A.2
  • 2
    • 0001560406 scopus 로고    scopus 로고
    • On the front-tracking algorithm
    • [BaJ]
    • [BaJ] P. BAITI and H. K. JENSSEN, On the front-tracking algorithm, J. Math. Anal. Appl. 217 (1998), 395-404.
    • (1998) J. Math. Anal. Appl. , vol.217 , pp. 395-404
    • Baiti, P.1    Jenssen, H.K.2
  • 3
    • 0035343172 scopus 로고    scopus 로고
    • Uniqueness of classical and nonclassical solutions for nonlinear hyperbolic systems
    • [BLFP]
    • [BLFP] P. BAITI, P. LEFLOCH, and B. PICCOLI, Uniqueness of classical and nonclassical solutions for nonlinear hyperbolic systems, J. Differential Equations 172 (2001), 59-82.
    • (2001) J. Differential Equations , vol.172 , pp. 59-82
    • Baiti, P.1    Lefloch, P.2    Piccoli, B.3
  • 4
    • 0012790248 scopus 로고    scopus 로고
    • BV estimates for a class of viscous hyperbolic systems
    • [BiB1]
    • [BiB1] S. BIANCHINI and A. BRESSAN, BV estimates for a class of viscous hyperbolic systems, Indiana Univ. Math. J. 49 (2000), 1673-1713.
    • (2000) Indiana Univ. Math. J. , vol.49 , pp. 1673-1713
    • Bianchini, S.1    Bressan, A.2
  • 5
    • 0036833129 scopus 로고    scopus 로고
    • On a Lyapunov functional relating shortening curves and conservation laws
    • [BiB2]
    • [BiB2] _, On a Lyapunov functional relating shortening curves and conservation laws, Nonlinear Anal., T.M.A. 51 (2002), 649-662.
    • (2002) Nonlinear Anal., T.M.A. , vol.51 , pp. 649-662
  • 6
    • 0035625301 scopus 로고    scopus 로고
    • A case study in vanishing viscosity
    • [BiB3]
    • [BiB3] _, A case study in vanishing viscosity, Discrete Contin. Dynam. Systems 7 (2001), 449-476.
    • (2001) Discrete Contin. Dynam. Systems , vol.7 , pp. 449-476
  • 7
    • 0012995480 scopus 로고    scopus 로고
    • A center manifold technique for tracing viscous waves
    • [BiB4]
    • [BiB4] _, A center manifold technique for tracing viscous waves, Comm. Pure Applied Anal. 1 (2002), 161-190.
    • (2002) Comm. Pure Applied Anal. , vol.1 , pp. 161-190
  • 8
    • 0001535322 scopus 로고
    • Contractive metrics for nonlinear hyperbolic systems
    • [B1]
    • [B1] A. BRESSAN, Contractive metrics for nonlinear hyperbolic systems, Indiana Univ. J. Math. 37 (1988), 409-421.
    • (1988) Indiana Univ. J. Math. , vol.37 , pp. 409-421
    • Bressan, A.1
  • 9
    • 38249009129 scopus 로고
    • Global solutions of systems of conservation laws by wave-front tracking
    • [B2]
    • [B2] _, Global solutions of systems of conservation laws by wave-front tracking, J. Math. Anal. Appl. 170 (1992), 414-432.
    • (1992) J. Math. Anal. Appl. , vol.170 , pp. 414-432
  • 10
    • 21844524094 scopus 로고
    • The unique limit of the Glimm scheme
    • [B3]
    • [B3] _, The unique limit of the Glimm scheme, Arch. Rational Mech. Anal. 130 (1995), 205-230.
    • (1995) Arch. Rational Mech. Anal. , vol.130 , pp. 205-230
  • 11
    • 0005513502 scopus 로고
    • A locally contractive metric for systems of conservation laws
    • [B4]
    • [B4] _, A locally contractive metric for systems of conservation laws, Ann. Scuola Norm. Sup. Pisa 22 (1995), 109-135.
    • (1995) Ann. Scuola Norm. Sup. Pisa , vol.22 , pp. 109-135
  • 13
    • 34247463858 scopus 로고
    • The semigroup generated by 2 × 2 conservation laws
    • [BC1]
    • [BC1] A. BRESSAN and R. M. COLOMBO, The semigroup generated by 2 × 2 conservation laws, Arch. Rational Mech. Anal. 133 (1995), 1-75.
    • (1995) Arch. Rational Mech. Anal. , vol.133 , pp. 1-75
    • Bressan, A.1    Colombo, R.M.2
  • 14
    • 0001412044 scopus 로고
    • Unique solutions of 2 × 2 conservation laws with large data
    • [BC2]
    • [BC2] _, Unique solutions of 2 × 2 conservation laws with large data, Indiana Univ. Math. J. 44 (1995), 677-725.
    • (1995) Indiana Univ. Math. J. , vol.44 , pp. 677-725
  • 15
    • 0006338644 scopus 로고    scopus 로고
    • Well-posedness of the cauchy problem for n × n conservation laws
    • [BCP]
    • [BCP] A. BRESSAN, G. CRASTA and B. PICCOLI, Well-Posedness of the Cauchy Problem for n × n Conservation Laws, Mem. Amer. Math. Soc. 694 (2000).
    • (2000) Mem. Amer. Math. Soc. , vol.694
    • Bressan, A.1    Crasta, G.2    Piccoli, B.3
  • 16
    • 0033587469 scopus 로고    scopus 로고
    • Oleinik type estimates and uniqueness for n × n conservation laws
    • [BG]
    • [BG] A. BRESSAN and P. GOATIN, Oleinik type estimates and uniqueness for n × n conservation laws, J. Differential Equations 156 (1999), 26-49.
    • (1999) J. Differential Equations , vol.156 , pp. 26-49
    • Bressan, A.1    Goatin, P.2
  • 17
    • 0031295331 scopus 로고    scopus 로고
    • Uniqueness of weak solutions to systems of conservation laws
    • [BLF1]
    • [BLF1] A. BRESSAN and P. LEFLOCH, Uniqueness of weak solutions to systems of conservation laws, Arch. Rational Mech. Anal. 140 (1997), 301-317.
    • (1997) Arch. Rational Mech. Anal. , vol.140 , pp. 301-317
    • Bressan, A.1    Lefloch, P.2
  • 18
    • 0013330827 scopus 로고    scopus 로고
    • Structural stability and regularity of entropy weak solutions to hyperbolic systems of conservation laws
    • [BLF2]
    • [BLF2] _, Structural stability and regularity of entropy weak solutions to hyperbolic systems of conservation laws, Indiana Univ. Math. J. 48 (1999), 43-84.
    • (1999) Indiana Univ. Math. J. , vol.48 , pp. 43-84
  • 19
    • 0034384317 scopus 로고    scopus 로고
    • A uniqueness condition for hyperbolic systems of conservation laws
    • [BLe]
    • [BLe] A. BRESSAN and M. LEWICKA, A uniqueness condition for hyperbolic systems of conservation laws, Discrete Contin. Dynam. Systems 6 (2000), 673-682.
    • (2000) Discrete Contin. Dynam. Systems , vol.6 , pp. 673-682
    • Bressan, A.1    Lewicka, M.2
  • 21
    • 0032343461 scopus 로고    scopus 로고
    • Uniqueness for discontinuous ODE and conservation laws
    • [BS]
    • [BS] A. BRESSAN and W. SHEN, Uniqueness for discontinuous ODE and conservation laws, Nonlinear Anal. 34 (1998), 637-652.
    • (1998) Nonlinear Anal. , vol.34 , pp. 637-652
    • Bressan, A.1    Shen, W.2
  • 23
    • 51249187580 scopus 로고
    • The semigroup approach to first order quasilinear equations in several space variables
    • [Cr]
    • [Cr] M. CRANDALL, The semigroup approach to first order quasilinear equations in several space variables, Israel J. Math. 12 (1972), 108-132.
    • (1972) Israel J. Math. , vol.12 , pp. 108-132
    • Crandall, M.1
  • 24
    • 0013425945 scopus 로고    scopus 로고
    • Hyperbolic conservation laws in continuum physics
    • [D], Springer-Verlag, New York
    • [D] C. DAFERMOS, Hyperbolic Conservation Laws in Continuum Physics, Grundlehren Math. Wiss. 325, Springer-Verlag, New York, 1999.
    • (1999) Grundlehren Math. Wiss. , vol.325
    • Dafermos, C.1
  • 25
    • 0001669027 scopus 로고
    • Global existence of solutions to nonlinear hyperbolic systems of conservation laws
    • [DP1]
    • [DP1] R. DIPERNA, Global existence of solutions to nonlinear hyperbolic systems of conservation laws, J. Differential Equations 20 (1976), 187-212.
    • (1976) J. Differential Equations , vol.20 , pp. 187-212
    • Diperna, R.1
  • 26
    • 0020499710 scopus 로고
    • Convergence of approximate solutions to conservation laws
    • [DP2]
    • [DP2] _, Convergence of approximate solutions to conservation laws, Arch. Rational Mech. Anal. 82 (1983), 27-70.
    • (1983) Arch. Rational Mech. Anal. , vol.82 , pp. 27-70
  • 28
    • 84980078812 scopus 로고
    • Steady-state solutions of hyperbolic systems of conservation laws with viscosity terms
    • [F]
    • [F] L. FOY, Steady-state solutions of hyperbolic systems of conservation laws with viscosity terms, Comm. Pure Appl. Math. 17 (1964), 177-188.
    • (1964) Comm. Pure Appl. Math. , vol.17 , pp. 177-188
    • Foy, L.1
  • 29
    • 84981759861 scopus 로고
    • Solutions in the large for nonlinear hyperbolic systems of equations
    • [G]
    • [G] J. GLIMM, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math. 18 (1965), 697-715.
    • (1965) Comm. Pure Appl. Math. , vol.18 , pp. 697-715
    • Glimm, J.1
  • 30
    • 21144475728 scopus 로고
    • Viscous limits for piecewise smooth solutions to systems of conservation laws
    • [GX]
    • [GX] J. GOODMAN and Z. XIN, Viscous limits for piecewise smooth solutions to systems of conservation laws, Arch. Rational Mech. Anal. 121 (1992), 235-265.
    • (1992) Arch. Rational Mech. Anal. , vol.121 , pp. 235-265
    • Goodman, J.1    Xin, Z.2
  • 31
    • 0034410383 scopus 로고    scopus 로고
    • 1 continuous dependence for systems of conservation laws
    • [HLF]
    • 1 continuous dependence for systems of conservation laws, Archive Rational Mech. Anal. 151 (2000), 45-93.
    • (2000) Archive Rational Mech. Anal. , vol.151 , pp. 45-93
    • Hu, J.1    Lefloch, P.G.2
  • 32
    • 0038336745 scopus 로고    scopus 로고
    • Existence theory for hyperbolic systems of conservation laws with general flux-functions
    • [ILF]
    • [ILF] T. IGUCHI and P. G. LEFLOCH, Existence theory for hyperbolic systems of conservation laws with general flux-functions, Arch. Rational Mech. Anal. 168 (2003), 165-244.
    • (2003) Arch. Rational Mech. Anal. , vol.168 , pp. 165-244
    • Iguchi, T.1    Lefloch, P.G.2
  • 33
    • 84956238079 scopus 로고
    • First-order quasilinear equations with several space variables
    • [Kr]
    • [Kr] S. KRUZHKOV, First-order quasilinear equations with several space variables, Math. USSR Sbornik 10 (1970), 217-243.
    • (1970) Math. USSR Sbornik , vol.10 , pp. 217-243
    • Kruzhkov, S.1
  • 34
    • 0034347315 scopus 로고    scopus 로고
    • Blowup for systems of conservation laws
    • [J]
    • [J] H. K. JENSSEN, Blowup for systems of conservation laws, SIAM J. Math. Anal. 31 (2000), 894-908.
    • (2000) SIAM J. Math. Anal. , vol.31 , pp. 894-908
    • Jenssen, H.K.1
  • 35
    • 84980077727 scopus 로고
    • Hyperbolic systems of conservation laws II
    • [Lx]
    • [Lx] P. LAX, Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math. 10 (1957), 537-566.
    • (1957) Comm. Pure Appl. Math. , vol.10 , pp. 537-566
    • Lax, P.1
  • 36
    • 0016890833 scopus 로고
    • The entropy condition and the admissibility of shocks
    • [L1]
    • [L1] T. P. Liu, The entropy condition and the admissibility of shocks, J. Math. Anal. Appl. 53 (1976), 78-88.
    • (1976) J. Math. Anal. Appl. , vol.53 , pp. 78-88
    • Liu, T.P.1
  • 37
    • 84980182288 scopus 로고
    • Decay to N-waves of solutions of general systems of nonlinear hyperbolic conservation laws
    • [L2]
    • [L2] T. P. Liu, Decay to N-waves of solutions of general systems of nonlinear hyperbolic conservation laws, Comm. Pure Appl. Math. 30 (1977), 586-611.
    • (1977) Comm. Pure Appl. Math. , vol.30 , pp. 586-611
    • Liu, T.P.1
  • 38
    • 84980187336 scopus 로고
    • Linear and nonlinear large-time behavior of solutions of general systems of hyperbolic conservation laws
    • [L3]
    • [L3] T. P. Liu, Linear and nonlinear large-time behavior of solutions of general systems of hyperbolic conservation laws, Comm. Pure Appl. Math. 30 (1977), 767-796.
    • (1977) Comm. Pure Appl. Math. , vol.30 , pp. 767-796
    • Liu, T.P.1
  • 39
    • 0003094236 scopus 로고
    • Admissible solutions of hyperbolic conservation laws
    • [L4]
    • [L4] _, Admissible Solutions of Hyperbolic Conservation Laws, Mem. Amer. Math. Soc. 240 (1981).
    • (1981) Mem. Amer. Math. Soc. , vol.240
  • 40
    • 0003343266 scopus 로고
    • Nonlinear stability of shock waves for viscous conservation laws
    • [L5]
    • [L5] _, Nonlinear Stability of Shock Waves for Viscous Conservation Laws, Mem. Amer. Math. Soc. 328 (1986).
    • (1986) Mem. Amer. Math. Soc. , vol.328
  • 41
    • 0033470637 scopus 로고    scopus 로고
    • A new entropy functional for a scalar conservation law
    • [LY1]
    • [LY1] T. P. Liu and T. YANG, A new entropy functional for a scalar conservation law, Comm. Pure Appl. Math. 52 (1999), 1427-1442.
    • (1999) Comm. Pure Appl. Math. , vol.52 , pp. 1427-1442
    • Liu, T.P.1    Yang, T.2
  • 42
    • 0346402790 scopus 로고    scopus 로고
    • 1 stability for 2 × 2 systems of hyperbolic conservation laws
    • [LY2]
    • 1 stability for 2 × 2 systems of hyperbolic conservation laws, J. Amer. Math. Soc. 12 (1999), 729-774.
    • (1999) J. Amer. Math. Soc. , vol.12 , pp. 729-774
  • 43
    • 0036026978 scopus 로고    scopus 로고
    • Weak solutions of general systems of hyperbolic conservation laws
    • [LY3]
    • [LY3] _, Weak solutions of general systems of hyperbolic conservation laws, Comm. Math. Phys. 230 (2002), 289-327.
    • (2002) Comm. Math. Phys. , vol.230 , pp. 289-327
  • 44
    • 0002124586 scopus 로고
    • Stable viscosity matrices for systems of conservation laws
    • [MP]
    • [MP] A. MAJDA and R. PEGO, Stable viscosity matrices for systems of conservation laws, J. Differential Equations 56 (1985), 229-262.
    • (1985) J. Differential Equations , vol.56 , pp. 229-262
    • Majda, A.1    Pego, R.2
  • 45
    • 0002717472 scopus 로고
    • Discontinuous solutions of non-linear differential equations
    • [O]
    • [O] O. OLEINIK, Discontinuous solutions of non-linear differential equations, Amer. Math. Soc. Transl. 26 (1963), 95-172.
    • (1963) Amer. Math. Soc. Transl. , vol.26 , pp. 95-172
    • Oleinik, O.1
  • 46
    • 84966257267 scopus 로고
    • A front-tracking alternative to the random choice method
    • [Ri]
    • [Ri] N. H. RISEBRO, A front-tracking alternative to the random choice method, Proc. Amer. Math. Soc. 117 (1993), 1125-1139.
    • (1993) Proc. Amer. Math. Soc. , vol.117 , pp. 1125-1139
    • Risebro, N.H.1
  • 47
    • 0001304520 scopus 로고
    • Sufficient conditions for local existence via Glimm's scheme for large BV data
    • [S]
    • [S] S. SCHOCHET, Sufficient conditions for local existence via Glimm's scheme for large BV data, J. Differential Equations 89 (1991), 317-354.
    • (1991) J. Differential Equations , vol.89 , pp. 317-354
    • Schochet, S.1
  • 49
    • 21144471868 scopus 로고
    • Nonlinear stability of viscous shock waves
    • [SX]
    • [SX] A. SZEPESSY and Z. XIN, Nonlinear stability of viscous shock waves, Arch. Rational Mech. Anal. 122 (1993), 53-103.
    • (1993) Arch. Rational Mech. Anal. , vol.122 , pp. 53-103
    • Szepessy, A.1    Xin, Z.2
  • 50
    • 0030533740 scopus 로고    scopus 로고
    • Stability of rarefaction waves in viscous media
    • [SZ]
    • [SZ] A. SZEPESSY and K. ZUMBRUN, Stability of rarefaction waves in viscous media, Arch. Rational Mech. Anal. 133 (1996), 249-298.
    • (1996) Arch. Rational Mech. Anal. , vol.133 , pp. 249-298
    • Szepessy, A.1    Zumbrun, K.2
  • 51
    • 0002876557 scopus 로고
    • Centre manifolds, normal forms and elementary bifurcations
    • [V]
    • [V] A. VANDERBAUWHEDE, Centre manifolds, normal forms and elementary bifurcations, Dynamics Reported 2 (1989), 89-169.
    • (1989) Dynamics Reported , vol.2 , pp. 89-169
    • Vanderbauwhede, A.1
  • 52
    • 0033416432 scopus 로고    scopus 로고
    • Zero-dissipation limit of solutions with shocks for systems of hyperbolic conservation laws
    • [Yu]
    • [Yu] S. H. Yu, Zero-dissipation limit of solutions with shocks for systems of hyperbolic conservation laws, Arch. Rational Mech. Anal. 146 (1999), 275-370.
    • (1999) Arch. Rational Mech. Anal. , vol.146 , pp. 275-370
    • Yu, S.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.