메뉴 건너뛰기




Volumn 8, Issue 1, 2005, Pages 1-20

The entropy principle: From continuum mechanics to hyperbolic systems of balance laws

Author keywords

[No Author keywords available]

Indexed keywords


EID: 14044278160     PISSN: 03924041     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (14)

References (37)
  • 1
    • 34250963757 scopus 로고
    • The thermomechanics of elastic materials with heat conduction and viscosity
    • B. D. COLEMAN - W. NOLL, The thermomechanics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal., 13 (1963), 167-178.
    • (1963) Arch. Rational Mech. Anal. , vol.13 , pp. 167-178
    • Coleman, B.D.1    Noll, W.2
  • 2
    • 0006989403 scopus 로고
    • On the entropy inequality
    • I. MÜLLER, On the entropy inequality, Arch. Rational Mech. Anal., 26 (1967), 118-141.
    • (1967) Arch. Rational Mech. Anal. , vol.26 , pp. 118-141
    • Müller, I.1
  • 4
    • 0002950929 scopus 로고
    • Shock waves and entropy
    • Ed. E. A. Zarantonello, New York, Academic Press
    • P. D. LAX, Shock Waves and Entropy, Contributions to Functional Analysis, 603-634, Ed. E. A. Zarantonello, New York, Academic Press (1971).
    • (1971) Contributions to Functional Analysis , pp. 603-634
    • Lax, P.D.1
  • 5
    • 0001380483 scopus 로고
    • Systems of conservation equations with a convex extension
    • K. O. FRIEDRICHS - P. D. LAX, Systems of conservation equations with a convex extension, Proc. Nat. Acad. Sci. USA, 68 (1971), 1686-1688.
    • (1971) Proc. Nat. Acad. Sci. USA , vol.68 , pp. 1686-1688
    • Friedrichs, K.O.1    Lax, P.D.2
  • 7
    • 0001513936 scopus 로고
    • The riemann problem for general system of conservation laws
    • T.-P. LIU, The Riemann Problem for General System of Conservation Laws, J. Differential Equations, 18 (1975), 218-234.
    • (1975) J. Differential Equations , vol.18 , pp. 218-234
    • Liu, T.-P.1
  • 8
    • 0003094236 scopus 로고
    • The admissible solutions of hyperbolic conservation laws
    • T.-P. LIU, The Admissible Solutions of Hyperbolic Conservation Laws, Memoir of AMS, 240 (1981), 78.
    • (1981) Memoir of AMS , vol.240 , pp. 78
    • Liu, T.-P.1
  • 9
    • 1342341863 scopus 로고    scopus 로고
    • Entropy production and admissibility of shocks
    • T.-P. LIU - T. RUGGERI, Entropy Production and Admissibility of Shocks, Acta Math. Appl. Sin., Engl. Ser., 19, No. 1 (2003), 1-12.
    • (2003) Acta Math. Appl. Sin., Engl. Ser. , vol.19 , Issue.1 , pp. 1-12
    • Liu, T.-P.1    Ruggeri, T.2
  • 10
    • 0001821191 scopus 로고
    • Main field and convex covariant density for quasi-linear hyperbolic systems. Relativistic fluid dynamics
    • T. RUGGERI - A. STRUMIA, Main field and convex covariant density for quasi-linear hyperbolic systems. Relativistic fluid dynamics, Ann. Inst. Henri Poincarè, 34-A (1981), 65-84.
    • (1981) Ann. Inst. Henri Poincarè , vol.34 A , pp. 65-84
    • Ruggeri, T.1    Strumia, A.2
  • 11
    • 0001675291 scopus 로고
    • Sur l'Existence et la Recherche d'Équations de Conservation Supplémentaires pour les Systèmes Hyperboliques
    • G. BOILLAT, Sur l'Existence et la Recherche d'Équations de Conservation Supplémentaires pour les Systèmes Hyperboliques, C.R. Acad. Sc. Paris, 278-A (1974), 909-912. Non Linear Fields and Waves. In CIME Course, Recent Mathematical Methods in Nonlinear Wave Propagation, Lecture Notes in Mathematics 1640, T. Ruggeri Ed. Springer-Verlag (1995), 103-152.
    • (1974) C.R. Acad. Sc. Paris , vol.278 A , pp. 909-912
    • Boillat, G.1
  • 12
    • 0040677527 scopus 로고
    • Non linear fields and waves
    • CIME Course, Recent Mathematical Methods in Nonlinear Wave Propagation, T. Ruggeri Ed. Springer-Verlag
    • G. BOILLAT, Sur l'Existence et la Recherche d'Équations de Conservation Supplémentaires pour les Systèmes Hyperboliques, C.R. Acad. Sc. Paris, 278-A (1974), 909-912. Non Linear Fields and Waves. In CIME Course, Recent Mathematical Methods in Nonlinear Wave Propagation, Lecture Notes in Mathematics 1640, T. Ruggeri Ed. Springer-Verlag (1995), 103-152.
    • (1995) Lecture Notes in Mathematics , vol.1640 , pp. 103-152
  • 13
    • 0001187980 scopus 로고
    • An interesting class of quasilinear systems
    • S. K. GODUNOV, An interesting class of quasilinear systems, Sov. Math., Dokl. 2 (1961), 947-949; translation from Dokl. Akad. Nauk SSSR, 139 (1961), 521-523.
    • (1961) Sov. Math., Dokl. , vol.2 , pp. 947-949
    • Godunov, S.K.1
  • 14
    • 0001631730 scopus 로고
    • S. K. GODUNOV, An interesting class of quasilinear systems, Sov. Math., Dokl. 2 (1961), 947-949; translation from Dokl. Akad. Nauk SSSR, 139 (1961), 521-523.
    • (1961) Dokl. Akad. Nauk SSSR , vol.139 , pp. 521-523
  • 15
    • 0031331292 scopus 로고    scopus 로고
    • Hyperbolic principal subsystems: Entropy convexity and sub characteristic conditions
    • G. BOILLAT - T. RUGGERI, Hyperbolic Principal Subsystems: Entropy Convexity and Sub characteristic Conditions, Arch. Rat. Mech. Anal., 137 (1997), 305-320.
    • (1997) Arch. Rat. Mech. Anal. , vol.137 , pp. 305-320
    • Boillat, G.1    Ruggeri, T.2
  • 16
    • 0032347251 scopus 로고    scopus 로고
    • On the shock structure problem for hyperbolic system of balance laws and convex entropy
    • G. BOILLAT - T. RUGGERI, On the shock structure problem for hyperbolic system of balance laws and convex entropy, Contin. Mech. Thermodyn., 10, No. 5 (1998), 285-292.
    • (1998) Contin. Mech. Thermodyn. , vol.10 , Issue.5 , pp. 285-292
    • Boillat, G.1    Ruggeri, T.2
  • 17
    • 0007423595 scopus 로고    scopus 로고
    • Maximum of entropy density in equilibrium and minimax principle for an hyperbolic system of balance laws
    • B. Albers editor WIAS-Report No. 18
    • T. RUGGERI, Maximum of Entropy Density in Equilibrium and Minimax Principle for an Hyperbolic System of Balance Laws, Contributions to Continuum Theories, Anniversary Volume for Krzysztoff Wilmanski, B. Albers editor WIAS-Report No. 18 (2000).
    • (2000) Contributions to Continuum Theories, Anniversary Volume for Krzysztoff Wilmanski
    • Ruggeri, T.1
  • 18
    • 14044268222 scopus 로고    scopus 로고
    • Stability of constant equilibrium state for dissipative balance laws system with a convex entropy
    • To appear
    • T. RUGGERI - D. SERRE, Stability of constant equilibrium state for dissipative balance laws system with a convex entropy, Quarterly of Applied Math. To appear (2003).
    • (2003) Quarterly of Applied Math.
    • Ruggeri, T.1    Serre, D.2
  • 19
    • 84976041027 scopus 로고
    • Large-time behavior of solutions to hyperbolic-parabolic systems of conservation laws and applications
    • S. KAWASHIMA, Large-time behavior of solutions to hyperbolic-parabolic systems of conservation laws and applications, Proc. R. Soc. Edinb., Sect. A, 106 (1987), 169-194.
    • (1987) Proc. R. Soc. Edinb., Sect. A , vol.106 , pp. 169-194
    • Kawashima, S.1
  • 20
    • 0003054750 scopus 로고
    • The Einstein evolution equations as a first-order quasi-linear symmetric hyperbolic system
    • A. E. FISCHER - J. E. MARSDEN, The Einstein evolution equations as a first-order quasi-linear symmetric hyperbolic system, Commun. Math. Phys., 28 (1972), 1-38.
    • (1972) Commun. Math. Phys. , vol.28 , pp. 1-38
    • Fischer, A.E.1    Marsden, J.E.2
  • 22
    • 0033275052 scopus 로고    scopus 로고
    • Gas dynamics in thermal nonequilibrium and general hyperbolic systems with relaxation
    • Y. ZENG, Gas dynamics in thermal nonequilibrium and general hyperbolic systems with relaxation, Arch. Ration. Mech. Anal., 150, No. 3 (1999), 225-279.
    • (1999) Arch. Ration. Mech. Anal. , vol.150 , Issue.3 , pp. 225-279
    • Zeng, Y.1
  • 23
    • 0141462542 scopus 로고    scopus 로고
    • Global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy
    • B. HANOUZET - R. NATALINI, Global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy, Arch. Rat. Mech. Anal., 169 (2003), 89-117.
    • (2003) Arch. Rat. Mech. Anal. , vol.169 , pp. 89-117
    • Hanouzet, B.1    Natalini, R.2
  • 24
    • 0004079016 scopus 로고    scopus 로고
    • Rational extended thermodynamics, 2nd ed.
    • Springer-Verlag, New York
    • I. MÜLLER - T. RUGGERI, Rational Extended Thermodynamics, 2nd ed., Springer Tracts in Natural Philosophy 37, Springer-Verlag, New York (1998).
    • (1998) Springer Tracts in Natural Philosophy , vol.37
    • Müller, I.1    Ruggeri, T.2
  • 25
    • 84980081651 scopus 로고
    • On the kinetic theory of rarefied gases
    • H. GRAD, On the kinetic theory of rarefied gases, Comm. Appl. Math., 2 (1949), 331-407.
    • (1949) Comm. Appl. Math. , vol.2 , pp. 331-407
    • Grad, H.1
  • 26
    • 0031519460 scopus 로고    scopus 로고
    • Moment equations in the kinetic theory of gases and wave velocities
    • G. BOILLAT - T. RUGGERI, Moment equations in the kinetic theory of gases and wave velocities, Contin. Mech. Thermodyn., 9, No. 4 (1997), 205-212.
    • (1997) Contin. Mech. Thermodyn. , vol.9 , Issue.4 , pp. 205-212
    • Boillat, G.1    Ruggeri, T.2
  • 27
    • 0033445708 scopus 로고    scopus 로고
    • Maximum wave velocity in the moments' system of a relativistic gas
    • G. BOILLAT - T. RUGGERI, Maximum wave velocity in the moments' system of a relativistic gas, Contin. Mech. Thermodyn., 11, No. 2 (1999), 107-111.
    • (1999) Contin. Mech. Thermodyn. , vol.11 , Issue.2 , pp. 107-111
    • Boillat, G.1    Ruggeri, T.2
  • 28
    • 0033249098 scopus 로고    scopus 로고
    • Relativistic gas: Moment equations and maximum wave velocity
    • G. BOILLAT - T. RUGGERI, Relativistic gas: Moment equations and maximum wave velocity, J. Math. Phys., 40, No. 12 (1999), 6399-6406.
    • (1999) J. Math. Phys. , vol.40 , Issue.12 , pp. 6399-6406
    • Boillat, G.1    Ruggeri, T.2
  • 29
    • 0033414615 scopus 로고    scopus 로고
    • Maximum velocity for wave propagation in a relativistic rarefied gas
    • F. BRINI - T. RUGGERI, Maximum velocity for wave propagation in a relativistic rarefied gas, Contin. Mech. Thermodyn., 11, No. 5 (1999), 331-538.
    • (1999) Contin. Mech. Thermodyn. , vol.11 , Issue.5 , pp. 331-538
    • Brini, F.1    Ruggeri, T.2
  • 31
    • 0002430565 scopus 로고
    • Light scattering and extended thermodynamics
    • W. WEISS - I. MÜLLER, Light scattering and extended thermodynamics, Cont. Mech. Thermodyn., 7 (1995), 123-144.
    • (1995) Cont. Mech. Thermodyn. , vol.7 , pp. 123-144
    • Weiss, W.1    Müller, I.2
  • 32
    • 0031185078 scopus 로고    scopus 로고
    • An extended moment method in radiative transfer: The matrices of mean absorption and scattering coefficients
    • H. STRUCHTRUP, An extended moment method in radiative transfer: The matrices of mean absorption and scattering coefficients, Annals of Physics, 257, No. 2 (1997), 111-135.
    • (1997) Annals of Physics , vol.257 , Issue.2 , pp. 111-135
    • Struchtrup, H.1
  • 33
    • 0039156111 scopus 로고    scopus 로고
    • Thermal conductivity and dynamic pressure in extended thermodynamics of chemically reacting mixtures of gases
    • G. M. KREMER - I. MÜLLER, Thermal conductivity and dynamic pressure in extended thermodynamics of chemically reacting mixtures of gases, Ann. Inst. Henri Poincarè, Phys. Théor., 69, No. 3 (1998), 309-334.
    • (1998) Ann. Inst. Henri Poincarè, Phys. Théor. , vol.69 , Issue.3 , pp. 309-334
    • Kremer, G.M.1    Müller, I.2
  • 34
    • 0034450587 scopus 로고    scopus 로고
    • Extended hydrodynamical model of carrier transport in semiconductors
    • A. M. ANILE - V. ROMANO - G. RUSSO, Extended hydrodynamical model of carrier transport in semiconductors, SIAM J. Appl. Math., 61, No. 1 (2000), 74-101.
    • (2000) SIAM J. Appl. Math. , vol.61 , Issue.1 , pp. 74-101
    • Anile, A.M.1    Romano, V.2    Russo, G.3
  • 35
    • 0001528492 scopus 로고
    • Maximisation of the entropy in non-equilibrium
    • W. DREYER, Maximisation of the Entropy in Non-Equilibrium, J. Phys. A: Math. Gen., 20 (1987), 6505-6512.
    • (1987) J. Phys. A: Math. Gen. , vol.20 , pp. 6505-6512
    • Dreyer, W.1
  • 36
    • 0001590042 scopus 로고
    • Breakdown of shock wave structure solutions
    • T. RUGGERI, Breakdown of Shock Wave Structure Solutions, Phys. Rev., 47-E, (6) (1993), 4135-4140.
    • (1993) Phys. Rev. , vol.47 E , Issue.6 , pp. 4135-4140
    • Ruggeri, T.1
  • 37
    • 0000213514 scopus 로고
    • Continuous shock structure in extended thermodynamics
    • W. WEISS, Continuous shock structure in extended thermodynamics, Phys. Review E, Part A, 52 (1995), 5760-5768.
    • (1995) Phys. Review E, Part A , vol.52 , pp. 5760-5768
    • Weiss, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.