메뉴 건너뛰기




Volumn 185, Issue 1, 2002, Pages 251-270

Weak entropy boundary conditions for isentropic gas dynamics via kinetic relaxation

Author keywords

Entropy boundary conditions; Isentropic gas dynamics; Kinetic BGK model; Kinetic entropy; Kinetic invariant domain; Relaxation limit; Weak trace

Indexed keywords


EID: 0037057999     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2001.4161     Document Type: Article
Times cited : (8)

References (34)
  • 1
    • 0002709803 scopus 로고    scopus 로고
    • Initial-boundary value problems for nonlinear systems of conservation laws
    • D. Amadori, Initial-boundary value problems for nonlinear systems of conservation laws, Nonlinear Differential Equations Applications 4 (1997), 1-42.
    • (1997) Nonlinear Differential Equations Applications , vol.4 , pp. 1-42
    • Amadori, D.1
  • 2
    • 0000978548 scopus 로고
    • Pairings between measures and bounded functions and compensated compactness
    • G. Anzellotti, Pairings between measures and bounded functions and compensated compactness, Ann. Mat. Pura Appl. 135 (1983), 293-318.
    • (1983) Ann. Mat. Pura Appl , vol.135 , pp. 293-318
    • Anzellotti, G.1
  • 5
    • 0001398501 scopus 로고
    • Problèmes aux limites pour des systèmes hyperboliques non linéaires de deux équations à une dimension d'espace
    • A. Benabdallah and D. Serre, Problèmes aux limites pour des systèmes hyperboliques non linéaires de deux équations à une dimension d'espace, C. R. Acad. Sci. Paris Sér. I Math. 305 (1987), 677-680.
    • (1987) C. R. Acad. Sci. Paris Sér. I Math , vol.305 , pp. 677-680
    • Benabdallah, A.1    Serre, D.2
  • 6
    • 0011630644 scopus 로고    scopus 로고
    • Solution with finite energy to a BGK system relaxing to isentropic gas dynamics
    • F. Berthelin and F. Bouchut, Solution with finite energy to a BGK system relaxing to isentropic gas dynamics, Ann. Fac. Sci. Toulouse 9 (2000), 605-630.
    • (2000) Ann. Fac. Sci. Toulouse , vol.9 , pp. 605-630
    • Berthelin, F.1    Bouchut, F.2
  • 7
    • 0036702873 scopus 로고    scopus 로고
    • Kinetic invariant domains and relaxation limit from a BGK model to isentropic gas dynamics
    • to appear
    • F. Berthelin and F. Bouchut, Kinetic invariant domains and relaxation limit from a BGK model to isentropic gas dynamics, Asymptotic Anal. (2002), to appear.
    • (2002) Asymptotic Anal
    • Berthelin, F.1    Bouchut, F.2
  • 8
    • 0033246851 scopus 로고    scopus 로고
    • Construction of BGK models with a family of kinetic entropies for a given system of conservation laws
    • F. Bouchut, Construction of BGK models with a family of kinetic entropies for a given system of conservation laws, J. Statist. Phys. 95 (1999), 113-170.
    • (1999) J. Statist. Phys , vol.95 , pp. 113-170
    • Bouchut, F.1
  • 9
    • 0035627821 scopus 로고    scopus 로고
    • Renormalized solutions to the Vlasov equation with coefficients of bounded variation
    • F. Bouchut, Renormalized solutions to the Vlasov equation with coefficients of bounded variation, Arch. Rational Mech. Anal. 157 (2001), 75-90.
    • (2001) Arch. Rational Mech. Anal , vol.157 , pp. 75-90
    • Bouchut, F.1
  • 10
    • 0001183792 scopus 로고    scopus 로고
    • A kinetic formulation for multi-branch entropy solutions of scalar conservation laws
    • Y. Brenier and L. Corrias, A kinetic formulation for multi-branch entropy solutions of scalar conservation laws, Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998), 169-190.
    • (1998) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.15 , pp. 169-190
    • Brenier, Y.1    Corrias, L.2
  • 11
    • 0033450362 scopus 로고    scopus 로고
    • Divergence-measure fields and hyperbolic conservation laws
    • G.-Q. Chen and H. Frid, Divergence-measure fields and hyperbolic conservation laws, Arch. Rational Mech. Anal. 147 (1999), 89-118.
    • (1999) Arch. Rational Mech. Anal , vol.147 , pp. 89-118
    • Chen, G.-Q.1    Frid, H.2
  • 12
    • 0002578353 scopus 로고
    • Convergence of the viscosity method for isentropic gas dynamics
    • R. J. DiPerna, Convergence of the viscosity method for isentropic gas dynamics, Comm. Math. Phys. 91 (1983), 1-30.
    • (1983) Comm. Math. Phys , vol.91 , pp. 1-30
    • DiPerna, R.J.1
  • 13
    • 0002447593 scopus 로고
    • Boundary conditions for nonlinear hyperbolic systems of conservation laws
    • F. Dubois and P. Le Floch, Boundary conditions for nonlinear hyperbolic systems of conservation laws, J. Differential Equations 71 (1988), 93-122.
    • (1988) J. Differential Equations , vol.71 , pp. 93-122
    • Dubois, F.1    Le Floch, L.2
  • 14
    • 0031514482 scopus 로고    scopus 로고
    • Conditions aux limites pour un système strictement hyperbolique fournies par le schéma de Godunov
    • M. Gisclon and D. Serre, Conditions aux limites pour un système strictement hyperbolique fournies par le schéma de Godunov, RAIRO Modèl. Math. Anal. Numér. 31 (1997), 359-380.
    • (1997) RAIRO Modèl. Math. Anal. Numér , vol.31 , pp. 359-380
    • Gisclon, M.1    Serre, D.2
  • 15
    • 0004051877 scopus 로고
    • Initial boundary value problems for hyperbolic systems of conservation laws
    • Thesis, Stanford University
    • J. B. Goodman, Initial boundary value problems for hyperbolic systems of conservation laws, Thesis, Stanford University, 1981.
    • (1981)
    • Goodman, J.B.1
  • 16
    • 0032359626 scopus 로고    scopus 로고
    • Convergence results for some conservation laws with a reflux boundary condition and a relaxation term arising in chemical engineering
    • F. James, Convergence results for some conservation laws with a reflux boundary condition and a relaxation term arising in chemical engineering, SIAM J. Math. Anal. 29 (1998), 1200-1223.
    • (1998) SIAM J. Math. Anal , vol.29 , pp. 1200-1223
    • James, F.1
  • 17
    • 0031184758 scopus 로고    scopus 로고
    • Initial-boundary value problem for conservation laws
    • P. T. Kan, M. Santos, and Z. Xin, Initial-boundary value problem for conservation laws, Comm. Math. Phys. 186 (1997), 701-730.
    • (1997) Comm. Math. Phys , vol.186 , pp. 701-730
    • Kan, P.T.1    Santos, M.2    Xin, Z.3
  • 18
    • 0030539239 scopus 로고    scopus 로고
    • Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates
    • P.-L. Lions, B. Perthame, and P.E. Souganidis, Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates, Comm. Pure Appl. Math. 49 (1996), 599-638.
    • (1996) Comm. Pure Appl. Math , vol.49 , pp. 599-638
    • Lions, P.-L.1    Perthame, B.2    Souganidis, P.E.3
  • 19
    • 84968518243 scopus 로고
    • A kinetic formulation of multidimensional scalar conservation laws and related equations
    • P.-L. Lions, B. Perthame, and E. Tadmor, A kinetic formulation of multidimensional scalar conservation laws and related equations, J. Amer. Math. Soc. 7 (1994), 169-191.
    • (1994) J. Amer. Math. Soc , vol.7 , pp. 169-191
    • Lions, P.-L.1    Perthame, B.2    Tadmor, E.3
  • 20
    • 34249763254 scopus 로고
    • Kinetic formulation of the isentropic gas dynamics and p-systems
    • P.-L. Lions, B. Perthame, and E. Tadmor, Kinetic formulation of the isentropic gas dynamics and p-systems, Comm. Math. Phys. 163 (1994), 415-431.
    • (1994) Comm. Math. Phys , vol.163 , pp. 415-431
    • Lions, P.-L.1    Perthame, B.2    Tadmor, E.3
  • 21
    • 0017440586 scopus 로고
    • Initial-boundary value problems for gas dynamics
    • T. P. Liu, Initial-boundary value problems for gas dynamics, Arch. Rational Mech. Anal. 64 (1977), 137-168.
    • (1977) Arch. Rational Mech. Anal , vol.64 , pp. 137-168
    • Liu, T.P.1
  • 22
    • 85031367449 scopus 로고    scopus 로고
    • Stability and convergence of discrete kinetic approximations to an initial-boundary value problem for conservation laws
    • to appear
    • V. Milišić, Stability and convergence of discrete kinetic approximations to an initial-boundary value problem for conservation laws, Proc. Amer. Math. Soc., to appear.
    • Proc. Amer. Math. Soc
    • Milišić, V.1
  • 23
    • 11544335821 scopus 로고    scopus 로고
    • A discrete kinetic approximation of entropy solutions to multidimensional scalar conservation laws
    • R. Natalini, A discrete kinetic approximation of entropy solutions to multidimensional scalar conservation laws, J. Differential Equations 148 (1998), 292-317.
    • (1998) J. Differential Equations , vol.148 , pp. 292-317
    • Natalini, R.1
  • 24
    • 0011571725 scopus 로고    scopus 로고
    • Convergence of a relaxation approximation to a boundary value problem for conservation laws
    • R. Natalini and A. Terracina, Convergence of a relaxation approximation to a boundary value problem for conservation laws, Comm. Partial Differential Equations, 26 (2001), 1235-1252.
    • (2001) Comm. Partial Differential Equations , vol.26 , pp. 1235-1252
    • Natalini, R.1    Terracina, A.2
  • 25
    • 0030240947 scopus 로고    scopus 로고
    • The initial-boundary value problems for hyperbolic conservation laws with relaxation
    • S. Nishibata, The initial-boundary value problems for hyperbolic conservation laws with relaxation, J. Differential Equations 130 (1996), 100-126.
    • (1996) J. Differential Equations , vol.130 , pp. 100-126
    • Nishibata, S.1
  • 26
    • 0000110333 scopus 로고
    • Mixed problems for nonlinear conservation laws
    • T. Nishida and J. Smoller, Mixed problems for nonlinear conservation laws, J. Differential Equations 23 (1977), 244-269.
    • (1977) J. Differential Equations , vol.23 , pp. 244-269
    • Nishida, T.1    Smoller, J.2
  • 27
    • 0033089731 scopus 로고    scopus 로고
    • Boundary conditions for scalar conservation laws from a kinetic point of view
    • A. Nouri, A. Omrane, and J. P. Vila, Boundary conditions for scalar conservation laws from a kinetic point of view, J. Statist. Phys. 94 (1999), 779-804.
    • (1999) J. Statist. Phys , vol.94 , pp. 779-804
    • Nouri, A.1    Omrane, A.2    Vila, J.P.3
  • 28
    • 0000234101 scopus 로고    scopus 로고
    • Initial-boundary value problem for a scalar conservation law
    • F. Otto, Initial-boundary value problem for a scalar conservation law, C. R. Acad. Sci. Paris Sér. I Math. 322 (1996), 729-734.
    • (1996) C. R. Acad. Sci. Paris Sér. I Math , vol.322 , pp. 729-734
    • Otto, F.1
  • 29
    • 0000741448 scopus 로고
    • A kinetic equation with kinetic entropy functions for scalar conservation laws
    • B. Perthame and E. Tadmor, 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
  • 30
    • 0034369177 scopus 로고    scopus 로고
    • Kinetic formulation for systems of two conservation laws and elastodynamics
    • B. Perthame and A. E. Tzavaras, Kinetic formulation for systems of two conservation laws and elastodynamics, Arch. Rational Mech. Anal. 155 (2000), 1-48.
    • (2000) Arch. Rational Mech. Anal , vol.155 , pp. 1-48
    • Perthame, B.1    Tzavaras, A.E.2
  • 31
    • 0000305292 scopus 로고    scopus 로고
    • Relaxation semi-linéaire et cinétique des systèmes de lois de conservation
    • D. Serre, Relaxation semi-linéaire et cinétique des systèmes de lois de conservation, Ann. Inst. H. Poincaré Anal Non Linéaire 17 (2000), 169-192.
    • (2000) Ann. Inst. H. Poincaré Anal Non Linéaire , vol.17 , pp. 169-192
    • Serre, D.1
  • 32
    • 0033425513 scopus 로고    scopus 로고
    • Materials with internal variables and relaxation to conservation laws
    • A.E. Tzavaras, Materials with internal variables and relaxation to conservation laws, Arch. Rational Mech. Anal. 146 (1999), 129-155.
    • (1999) Arch. Rational Mech. Anal , vol.146 , pp. 129-155
    • Tzavaras, A.E.1
  • 33
    • 23044529677 scopus 로고    scopus 로고
    • Strong traces for solutions to multidimensional scalar conservation laws
    • A. Vasseur, Strong traces for solutions to multidimensional scalar conservation laws, Arch. Ration. Mech. Anal 160 (2001), 181-193.
    • (2001) Arch. Ration. Mech. Anal , vol.160 , pp. 181-193
    • Vasseur, A.1
  • 34
    • 0032362176 scopus 로고    scopus 로고
    • Asymptotic limit of initial-boundary value problems for conservation laws with relaxational extensions
    • W.-C. Wang and Z. Xin, Asymptotic limit of initial-boundary value problems for conservation laws with relaxational extensions, Comm. Pure Appl. Math. 51 (1998), 505-535.
    • (1998) Comm. Pure Appl. Math , vol.51 , pp. 505-535
    • Wang, W.-C.1    Xin, Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.