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Volumn 3, Issue 2, 2005, Pages 119-132

RELATIVE ENTROPY IN HYPERBOLIC RELAXATION*

Author keywords

relative entropy; relaxation limits

Indexed keywords


EID: 66049156332     PISSN: 15396746     EISSN: 19450796     Source Type: Journal    
DOI: 10.4310/CMS.2005.v3.n2.a2     Document Type: Article
Times cited : (54)

References (17)
  • 1
    • 25444433067 scopus 로고    scopus 로고
    • Stability and convergence of a class of finite element schemes for hyperbolic systems of conservation laws
    • [1]
    • [1] Ch. Arvanitis, Ch. Makridakis and A. E. Tzavaras, Stability and convergence of a class of finite element schemes for hyperbolic systems of conservation laws, SIAM J. Numer. Analysis, 42, 1357-1393, 2004.
    • (2004) SIAM J. Numer. Analysis , vol.42 , pp. 1357-1393
    • Arvanitis, Ch.1    Makridakis, Ch.2    Tzavaras, A. E.3
  • 2
    • 85129267457 scopus 로고    scopus 로고
    • From kinetic equations to multidimensional isentropic gas dynamics before shocks
    • [2] to appear
    • [2] F. Berthelin and A. Vasseur, From kinetic equations to multidimensional isentropic gas dynamics before shocks, SIAM J. Math. Anal., to appear.
    • SIAM J. Math. Anal
    • Berthelin, F.1    Vasseur, A.2
  • 3
    • 0000373558 scopus 로고    scopus 로고
    • Convergence of the Vlasov-Poisson system to the incompressible Euler equations
    • [3]
    • [3] Y. Brenier, Convergence of the Vlasov-Poisson system to the incompressible Euler equations, Comm. Partial Diff. Equations, 25, 737-754, 2000.
    • (2000) Comm. Partial Diff. Equations , vol.25 , pp. 737-754
    • Brenier, Y.1
  • 4
    • 1642330013 scopus 로고    scopus 로고
    • On a relaxation approximation of the incompressible Navier-Stokes equations
    • [4]
    • [4] Y. Brenier, R. Natalini and M. Puel, On a relaxation approximation of the incompressible Navier-Stokes equations, Proc. Amer. Math. Soc., 132, 1021-1028, 2004.
    • (2004) Proc. Amer. Math. Soc , vol.132 , pp. 1021-1028
    • Brenier, Y.1    Natalini, R.2    Puel, M.3
  • 5
    • 0033246851 scopus 로고    scopus 로고
    • Construction of BGK models with a family of kinetic entropies for a given system of conservation laws
    • [5]
    • [5] F. Bouchut, Construction of BGK models with a family of kinetic entropies for a given system of conservation laws, J. Stat. Physics, 95, 113-170, 1999.
    • (1999) J. Stat. Physics , vol.95 , pp. 113-170
    • Bouchut, F.1
  • 6
    • 33745291057 scopus 로고    scopus 로고
    • A reduced stability condition for nonlinear relaxation to conservation laws
    • [6]
    • [6] F. Bouchut, A reduced stability condition for nonlinear relaxation to conservation laws,J. Hyperbolic Diff. Equations, 1, 149-170, 2004.
    • (2004) J. Hyperbolic Diff. Equations , vol.1 , pp. 149-170
    • Bouchut, F.1
  • 7
    • 84980139661 scopus 로고
    • The fluid-dynamical limit of a nonlinear model Boltzmann equation
    • [7]
    • [7] R. Caflisch and G. Papanicolaou, The fluid-dynamical limit of a nonlinear model Boltzmann equation, Comm. Pure Appl. Math., 32, 589-616, 1979.
    • (1979) Comm. Pure Appl. Math , vol.32 , pp. 589-616
    • Caflisch, R.1    Papanicolaou, G.2
  • 8
    • 84990689276 scopus 로고
    • Hyperbolic conservation laws with stiff relaxation terms and entropy
    • [8]
    • [8] G. Q. Chen, C. D. Levermore and T. P. Liu, Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure and Appl. Math., 47, 787—830, 1994.
    • (1994) Comm. Pure and Appl. Math , vol.47 , pp. 787-830
    • Chen, G. Q.1    Levermore, C. D.2    Liu, T. P.3
  • 9
    • 0018678304 scopus 로고
    • The second law of thermodynamics and stability
    • [9]
    • [9] C. M. Dafermos, The second law of thermodynamics and stability, Arch. Rational Mech. Anal., 70, 167-179, 1979.
    • (1979) Arch. Rational Mech. Anal , vol.70 , pp. 167-179
    • Dafermos, C. M.1
  • 10
    • 0013425945 scopus 로고    scopus 로고
    • Hyperbolic conservation laws in continuum physics
    • [10] Springer-Verlag, Berlin
    • [10] C. M. Dafermos, Hyperbolic conservation laws in continuum physics, Grundlehren der Mathe matischen Wissenschaften, Springer-Verlag, Berlin, 325, 2000.
    • (2000) Grundlehren der Mathe matischen Wissenschaften , pp. 325
    • Dafermos, C. M.1
  • 11
    • 0000408106 scopus 로고
    • Uniqueness of solutions to hyperbolic conservation laws
    • [11]
    • [11] R. J. DiPerna, Uniqueness of solutions to hyperbolic conservation laws, Indiana Univ. Math. J., 28, 137-188, 1979.
    • (1979) Indiana Univ. Math. J , vol.28 , pp. 137-188
    • DiPerna, R. J.1
  • 12
    • 0141462542 scopus 로고    scopus 로고
    • Global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy
    • [12]
    • [12] B. Hanouzet and R. Natalini, Global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy, Arch. Rational Mech. Anal., 169, 89-117, 2003.
    • (2003) Arch. Rational Mech. Anal , vol.169 , pp. 89-117
    • Hanouzet, B.1    Natalini, R.2
  • 13
    • 0000282942 scopus 로고    scopus 로고
    • Contractive relaxation systems and the scalar multidi mensional conservation law
    • [13]
    • [13] M. A. Katsoulakis and A. E. Tzavaras, Contractive relaxation systems and the scalar multidi mensional conservation law, Comm. Partial Diff. Equations, 22, 195-233, 1997.
    • (1997) Comm. Partial Diff. Equations , vol.22 , pp. 195-233
    • Katsoulakis, M. A.1    Tzavaras, A. E.2
  • 15
    • 0033425513 scopus 로고    scopus 로고
    • Materials with internal variables and relaxation to conservation laws
    • [15]
    • [15] A. E. Tzavaras, Materials with internal variables and relaxation to conservation laws, Arch. Rational Mech. Anal., 146, 129-155, 1999.
    • (1999) Arch. Rational Mech. Anal , vol.146 , pp. 129-155
    • Tzavaras, A. E.1
  • 16
    • 0033542203 scopus 로고    scopus 로고
    • Singular perturbations of first-order hyperbolic systems with stiff source terms
    • [16]
    • [16] W. A. Yong, Singular perturbations of first-order hyperbolic systems with stiff source terms, J. Differential Equations, 155, 89-132, 1999.
    • (1999) J. Differential Equations , vol.155 , pp. 89-132
    • Yong, W. A.1
  • 17
    • 2442700294 scopus 로고    scopus 로고
    • Entropy and global existence for hyperbolic balance laws
    • [17]
    • [17] W. A. Yong, Entropy and global existence for hyperbolic balance laws, Arch. Rational Mech. Anal., 172, 247-266, 2004.
    • (2004) Arch. Rational Mech. Anal , vol.172 , pp. 247-266
    • Yong, W. A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.