메뉴 건너뛰기




Volumn 180, Issue 3, 2006, Pages 449-492

Structural properties of stress relaxation and convergence from viscoelasticity to polyconvex elastodynamics

Author keywords

[No Author keywords available]

Indexed keywords


EID: 33645664054     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-005-0404-3     Document Type: Article
Times cited : (29)

References (24)
  • 1
    • 25444433067 scopus 로고    scopus 로고
    • Stability and convergence of a class of finite element schemes for hyperbolic systems of conservation laws
    • ARVANITIS, CH., MAKRIDAKIS, CH., TZAVARAS, A.E.: Stability and convergence of a class of finite element schemes for hyperbolic systems of conservation laws. SIAM J. Numer. Anal. 42, 1357-1393 (2004)
    • (2004) SIAM J. Numer. Anal. , vol.42 , pp. 1357-1393
    • Arvanitis, C.H.1    Makridakis, C.H.2    Tzavaras, A.E.3
  • 2
    • 0017417265 scopus 로고
    • Convexity conditions and existence theorems in the nonlinear elasticity
    • BALL, J.M.: Convexity conditions and existence theorems in the nonlinear elasticity. Arch. Ration. Mech. Anal. 63, 337-403 (1977)
    • (1977) Arch. Ration. Mech. Anal. , vol.63 , pp. 337-403
    • Ball, J.M.1
  • 3
    • 0012785350 scopus 로고    scopus 로고
    • Some open problems in elasticity
    • Springer, New York
    • BALL, J.M.: Some open problems in elasticity. In: Geometry, mechanics and dynamics, Springer, New York, 2002, pp. 3-59
    • (2002) Geometry, Mechanics and Dynamics , pp. 3-59
    • Ball, J.M.1
  • 4
    • 2142762359 scopus 로고    scopus 로고
    • Hydrodynamic structure of the augmented Born-Infeld equations
    • BRENIER, Y.: Hydrodynamic structure of the augmented Born-Infeld equations. Arch. Ration. Mech. Anal. 172, 65-91 (2004)
    • (2004) Arch. Ration. Mech. Anal. , vol.172 , pp. 65-91
    • Brenier, Y.1
  • 5
    • 1642330013 scopus 로고    scopus 로고
    • On a relaxation approximation of the incompressible Navier - Stokes equations
    • BRENIER, Y., NATALINI, R., PUEL, M.: 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
  • 6
    • 84980139661 scopus 로고
    • The fluid dynamical limit of a nonlinear model Boltzmann equation
    • CAFLISCH, R., PAPANICOLAOU, G.C.: 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.C.2
  • 7
    • 84990689276 scopus 로고
    • Hyperbolic conservation laws with stiff relaxation terms and entropy
    • CHEN, G.-Q., LEVERMORE, C.D., LIU, T.-P.: Hyperbolic conservation laws with stiff relaxation terms and entropy. Comm. Pure Appl. Math. 47, 787-830 (1994)
    • (1994) Comm. Pure Appl. Math. , vol.47 , pp. 787-830
    • Chen, G.-Q.1    Levermore, C.D.2    Liu, T.-P.3
  • 8
    • 0012607270 scopus 로고
    • Mathematical elasticity. Vol. I. Three - Dimensional elasticity
    • North - Holland
    • CIARLET, P.O.: Mathematical Elasticity. Vol. I. Three - dimensional elasticity. Studies in Mathematics and its Applications, vol. 20, North - Holland, 1988
    • (1988) Studies in Mathematics and Its Applications , vol.20
    • Ciarlet, P.O.1
  • 9
    • 36849104050 scopus 로고
    • Thermodynamics with internal state variables
    • COLEMAN, B.D., GURTIN, M.E.: Thermodynamics with internal state variables. J. Chem. Phys. 47, 597-613 (1967)
    • (1967) J. Chem. Phys. , vol.47 , pp. 597-613
    • Coleman, B.D.1    Gurtin, M.E.2
  • 10
    • 0001130290 scopus 로고    scopus 로고
    • Relaxation of energy and approximate Riemann solvers for general pressure laws in fluid dynamics
    • COQUEL, F., PERTHAME, B.: Relaxation of energy and approximate Riemann solvers for general pressure laws in fluid dynamics. SIAM J. Numer. Anal. 35, 2223-2249 (1998)
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 2223-2249
    • Coquel, F.1    Perthame, B.2
  • 11
    • 0018678304 scopus 로고
    • The second law of thermodynamics and stability
    • DAFERMOS, C.M.: The second law of thermodynamics and stability. Arch. Ration. Mech. Anal. 70, 167-179 (1979)
    • (1979) Arch. Ration. Mech. Anal. , vol.70 , pp. 167-179
    • Dafermos, C.M.1
  • 12
    • 0039334858 scopus 로고
    • Quasilinear hyperbolic systems with involutions
    • DAFERMOS, C.M.: Quasilinear hyperbolic systems with involutions. Arch. Ration. Mech. Anal. 94, 373-389 (1986)
    • (1986) Arch. Ration. Mech. Anal. , vol.94 , pp. 373-389
    • Dafermos, C.M.1
  • 13
    • 0013425945 scopus 로고    scopus 로고
    • Hyperbolic conservation laws in continuum physics
    • Springer-Verlag, Berlin
    • DAFERMOS, C.M.: Hyperbolic conservation laws in continuum physics. Grund lehren der Mathematischen Wissenschaften, vol. 325, Springer-Verlag, Berlin, 2000
    • (2000) Grund Lehren der Mathematischen Wissenschaften , vol.325
    • Dafermos, C.M.1
  • 14
    • 33645684967 scopus 로고    scopus 로고
    • Chapter V of 2nd edition of [13], (private communication)
    • DAFERMOS, C.M.: Chapter V of 2nd edition of [13], (private communication)
    • Dafermos, C.M.1
  • 15
    • 0035633712 scopus 로고    scopus 로고
    • A variational approximation scheme for three - Dimensional elastodynamics with polyconvex energy
    • DEMOULINI, S., STUART, D.M.A., TZAVARAS, A.E.: A variational approximation scheme for three - dimensional elastodynamics with polyconvex energy. Arch. Ration. Mech. Anal. 157, 325-344 (2001)
    • (2001) Arch. Ration. Mech. Anal. , vol.157 , pp. 325-344
    • Demoulini, S.1    Stuart, D.M.A.2    Tzavaras, A.E.3
  • 16
    • 0023533132 scopus 로고
    • The energy in one-dimensional rate-type semilinear viscoelasticity
    • FACIU, C., MIHAILESCU-SULICIU, M.: The energy in one-dimensional rate-type semilinear viscoelasticity. Internat. J. Solids Structures 23, 1505-1520 (1987)
    • (1987) Internat. J. Solids Structures , vol.23 , pp. 1505-1520
    • Faciu, C.1    Mihailescu-Suliciu, M.2
  • 17
    • 0035536415 scopus 로고    scopus 로고
    • Regularization of the Burnett equations via relaxation
    • JIN, S., SLEMROD, M.: Regularization of the Burnett equations via relaxation. J. Statist. Phys. 103, 1009-1033 (2001)
    • (2001) J. Statist. Phys. , vol.103 , pp. 1009-1033
    • Jin, S.1    Slemrod, M.2
  • 18
    • 0032304163 scopus 로고    scopus 로고
    • Symmetrizing nonlinear elastodynamic system
    • QIN, T.: Symmetrizing nonlinear elastodynamic system. J. Elasticity 50, 245-252 (1998)
    • (1998) J. Elasticity , vol.50 , pp. 245-252
    • Qin, T.1
  • 20
    • 3042671396 scopus 로고    scopus 로고
    • Hyperbolicity of the nonlinear models of maxwell's equations
    • SERRE, D.: Hyperbolicity of the Nonlinear Models of Maxwell's Equations. Arch. Ration. Mech. Anal. 172, 309-331 (2004)
    • (2004) Arch. Ration. Mech. Anal. , vol.172 , pp. 309-331
    • Serre, D.1
  • 21
    • 0032108863 scopus 로고    scopus 로고
    • On the thermodynamics of rate-type fluids and phase transitions. I. Rate-type fluids
    • SULICIU, I.: On the thermodynamics of rate-type fluids and phase transitions. I. Rate-type fluids. Internat. J. Engrg. Sci. 36, 921-947 (1998)
    • (1998) Internat. J. Engrg. Sci. , vol.36 , pp. 921-947
    • Suliciu, I.1
  • 22
    • 0033425513 scopus 로고    scopus 로고
    • Materials with internal variables and relaxation to conservation laws
    • TZAVARAS, A.: Materials with Internal Variables and Relaxation to Conservation Laws. Arch. Ration. Mech. Anal. 146, 129-155 (1999)
    • (1999) Arch. Ration. Mech. Anal. , vol.146 , pp. 129-155
    • Tzavaras, A.1
  • 23
    • 0033542203 scopus 로고    scopus 로고
    • Singular perturbations of first-order hyperbolic systems with stiff source terms
    • YONG, W.A.: 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
  • 24
    • 0033275052 scopus 로고    scopus 로고
    • Gas dynamics in thermal nonequilibrium and general hyperbolic systems with relaxation
    • ZENG, Y.: Gas dynamics in thermal nonequilibrium and general hyperbolic systems with relaxation. Arch. Ration. Mech. Anal. 150, 225-279 (1999)
    • (1999) Arch. Ration. Mech. Anal. , vol.150 , pp. 225-279
    • Zeng, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.