메뉴 건너뛰기




Volumn 245, Issue 11, 2008, Pages 3095-3126

Hyperbolic conservation laws with discontinuous fluxes and hydrodynamic limit for particle systems

Author keywords

Compactness framework; Discontinuous flux functions; Discontinuous speed parameter; Entropy conditions; Entropy solutions; Hydrodynamic limits; Hyperbolic conservation laws; Measure valued; Microscopic; Particle systems; Uniqueness; Zero range process

Indexed keywords


EID: 53349167256     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2008.07.036     Document Type: Article
Times cited : (30)

References (26)
  • 1
  • 2
    • 17744396698 scopus 로고    scopus 로고
    • Uniqueness for a scalar conservation law with discontinuous flux via adapted entropies
    • Audusse E., and Perthame B. Uniqueness for a scalar conservation law with discontinuous flux via adapted entropies. Proc. Roy. Soc. Edinburgh Sect. A 135 (2005) 253-265
    • (2005) Proc. Roy. Soc. Edinburgh Sect. A , vol.135 , pp. 253-265
    • Audusse, E.1    Perthame, B.2
  • 3
    • 0032021366 scopus 로고    scopus 로고
    • Hydrodynamic limit for spatially heterogeneous simple exclusion processes
    • Bahadoran C. Hydrodynamic limit for spatially heterogeneous simple exclusion processes. Probab. Theory Related Fields 110 (1998) 287-331
    • (1998) Probab. Theory Related Fields , vol.110 , pp. 287-331
    • Bahadoran, C.1
  • 5
    • 53349100666 scopus 로고    scopus 로고
    • R. Bürger, K.H. Karlsen, J.D. Tower, An Engquist-Osher-type scheme for conservation laws with discontinuous flux adapted to flux connections, 2007, submitted for publication; available at: http://www.math.ntnu.no/conservation/
    • R. Bürger, K.H. Karlsen, J.D. Tower, An Engquist-Osher-type scheme for conservation laws with discontinuous flux adapted to flux connections, 2007, submitted for publication; available at: http://www.math.ntnu.no/conservation/
  • 6
    • 53349096363 scopus 로고    scopus 로고
    • G.-Q. Chen, The compensated compactness method and the system of isentropic gas dynamics, Lecture Notes, Preprint MSRI-00527-91, Berkeley, October 1990
    • G.-Q. Chen, The compensated compactness method and the system of isentropic gas dynamics, Lecture Notes, Preprint MSRI-00527-91, Berkeley, October 1990
  • 7
    • 66149149400 scopus 로고    scopus 로고
    • Euler equations and related hyperbolic conservation laws
    • Dafermos C.M., and Feireisl E. (Eds), Elsevier, Amsterdam (Chapter 1)
    • Chen G.-Q. Euler equations and related hyperbolic conservation laws. In: Dafermos C.M., and Feireisl E. (Eds). Handbook of Differential Equations, vol. 2 (2005), Elsevier, Amsterdam 1-104 (Chapter 1)
    • (2005) Handbook of Differential Equations, vol. 2 , pp. 1-104
    • Chen, G.-Q.1
  • 8
    • 0034373046 scopus 로고    scopus 로고
    • Initial layers and uniqueness of weak entropy solutions to hyperbolic conservation laws
    • Chen G.-Q., and Rascle M. Initial layers and uniqueness of weak entropy solutions to hyperbolic conservation laws. Arch. Ration. Mech. Anal. 153 (2000) 205-220
    • (2000) Arch. Ration. Mech. Anal. , vol.153 , pp. 205-220
    • Chen, G.-Q.1    Rascle, M.2
  • 11
    • 0008707653 scopus 로고
    • Processus des misanthropes
    • Cocozza C.T. Processus des misanthropes. Z. Wahrsch. Verw. Geb. 70 (1985) 509-523
    • (1985) Z. Wahrsch. Verw. Geb. , vol.70 , pp. 509-523
    • Cocozza, C.T.1
  • 12
    • 0031184716 scopus 로고    scopus 로고
    • Hydrodynamic limit for particle systems with nonconstant speed parameter
    • Covert P., and Rezakhanlou F. Hydrodynamic limit for particle systems with nonconstant speed parameter. J. Stat. Phys. 88 (1997) 383-426
    • (1997) J. Stat. Phys. , vol.88 , pp. 383-426
    • Covert, P.1    Rezakhanlou, F.2
  • 13
    • 0000298704 scopus 로고
    • Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics (I)-(II)
    • 501-540 (in English)
    • Ding X., Chen G.-Q., and Luo P. Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics (I)-(II). Acta Math. Sci. 5 (1985) 483-500 501-540 (in English)
    • (1985) Acta Math. Sci. , vol.5 , pp. 483-500
    • Ding, X.1    Chen, G.-Q.2    Luo, P.3
  • 14
    • 0000729068 scopus 로고
    • Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics (I)-(II)
    • Ding X., Chen G.-Q., and Luo P. Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics (I)-(II). Acta Math. Sci. 7 (1987) 467-480
    • (1987) Acta Math. Sci. , vol.7 , pp. 467-480
    • Ding, X.1    Chen, G.-Q.2    Luo, P.3
  • 15
    • 27144524008 scopus 로고
    • Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics (I)-(II)
    • (in Chinese)
    • Ding X., Chen G.-Q., and Luo P. Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics (I)-(II). Acta Math. Sci. 8 (1988) 61-94 (in Chinese)
    • (1988) Acta Math. Sci. , vol.8 , pp. 61-94
    • Ding, X.1    Chen, G.-Q.2    Luo, P.3
  • 16
    • 0021835204 scopus 로고
    • Measure-valued solutions to conservation laws
    • DiPerna R.J. Measure-valued solutions to conservation laws. Arch. Ration. Mech. Anal. 88 (1985) 223-270
    • (1985) Arch. Ration. Mech. Anal. , vol.88 , pp. 223-270
    • DiPerna, R.J.1
  • 17
    • 4444234405 scopus 로고    scopus 로고
    • 1 stability for entropy solutions of nonlinear degenerate parabolic convection diffusion equations with discontinuous coefficients
    • 1 stability for entropy solutions of nonlinear degenerate parabolic convection diffusion equations with discontinuous coefficients. Skr. K. Nor. Vidensk. Selsk. 3 (2003) 1-49
    • (2003) Skr. K. Nor. Vidensk. Selsk. , vol.3 , pp. 1-49
    • Karlsen, K.H.1    Risebro, N.H.2    Towers, J.3
  • 20
    • 84956238079 scopus 로고
    • First order quasilinear equations in several independent variables
    • Kruzkov S.N. First order quasilinear equations in several independent variables. Math. USSR Sb. 10 (1970) 217-243
    • (1970) Math. USSR Sb. , vol.10 , pp. 217-243
    • Kruzkov, S.N.1
  • 22
    • 0001764754 scopus 로고
    • - 1, q is completely continuous for all q < 2
    • - 1, q is completely continuous for all q < 2. J. Math. Pures Appl. (9) 60 (1981) 309-322
    • (1981) J. Math. Pures Appl. (9) , vol.60 , pp. 309-322
    • Murat, F.1
  • 23
    • 53349167117 scopus 로고    scopus 로고
    • E.Yu. Panov, Existence and strong pre-compactness properties for entropy solutions of a first-order quasilinear equation with discontinuous flux, preprint, 2007, available at: http://www.math.ntnu.no/conservation/
    • E.Yu. Panov, Existence and strong pre-compactness properties for entropy solutions of a first-order quasilinear equation with discontinuous flux, preprint, 2007, available at: http://www.math.ntnu.no/conservation/
  • 25
    • 0000440966 scopus 로고
    • Compensated compactness and applications to partial differential equations
    • Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, vol. 4, Pitman, Boston, MA, London
    • Tartar L. Compensated compactness and applications to partial differential equations. Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, vol. 4. Res. Notes Math. vol. 39 (1979), Pitman, Boston, MA, London 136-212
    • (1979) Res. Notes Math. , vol.39 , pp. 136-212
    • Tartar, L.1
  • 26
    • 0003135582 scopus 로고
    • Relative entropy and hydrodynamics of Ginzburg-Landau models
    • Yau H.T. Relative entropy and hydrodynamics of Ginzburg-Landau models. Lett. Math. Phys. 22 1 (1991) 63-80
    • (1991) Lett. Math. Phys. , vol.22 , Issue.1 , pp. 63-80
    • Yau, H.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.