메뉴 건너뛰기




Volumn 175, Issue 1, 2005, Pages 85-150

The parabolic-hyperbolic system governing the spatial motion of nonlinearly viscoelastic rods

Author keywords

[No Author keywords available]

Indexed keywords


EID: 12444281838     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00205-004-0341-6     Document Type: Article
Times cited : (23)

References (44)
  • 3
    • 58149411463 scopus 로고
    • Asymptotic behaviour and changes of phase in one-dimensional nonlinear viscoelasticity
    • ANDREWS, G., BALL, J.M.: Asymptotic behaviour and changes of phase in one-dimensional nonlinear viscoelasticity. J. Diff. Eqs. 44, 306-341 (1982)
    • (1982) J. Diff. Eqs. , vol.44 , pp. 306-341
    • Andrews, G.1    Ball, J.M.2
  • 4
    • 0017132844 scopus 로고
    • Ordinary differential equations of one-dimensional nonlinear elasticity II: Existence and regularity theory for conservative problems
    • ANTMAN, S.S.: Ordinary differential equations of one-dimensional nonlinear elasticity II: Existence and regularity theory for conservative problems. Arch. Rational Mech. Anal. 61, 353-393 (1976)
    • (1976) Arch. Rational Mech. Anal. , vol.61 , pp. 353-393
    • Antman, S.S.1
  • 6
    • 0346255333 scopus 로고    scopus 로고
    • Invariant dissipative mechanisms for the spatial motion of rods suggested by artificial viscosity
    • ANTMAN, S.S.: Invariant dissipative mechanisms for the spatial motion of rods suggested by artificial viscosity. J. Elasticity 70, 55-64 (2003)
    • (2003) J. Elasticity , vol.70 , pp. 55-64
    • Antman, S.S.1
  • 8
    • 0019668063 scopus 로고
    • Large buckled states of nonlinearly elastic rods under torsion, thrust, and gravity
    • ANTMAN, S.S., KENNEY, C.S.: Large buckled states of nonlinearly elastic rods under torsion, thrust, and gravity. Arch. Rational Mech. Anal. 76, 289-338 (1981)
    • (1981) Arch. Rational Mech. Anal. , vol.76 , pp. 289-338
    • Antman, S.S.1    Kenney, C.S.2
  • 9
    • 0033713213 scopus 로고    scopus 로고
    • Self-sustained oscillations of nonlinearly viscoelastic layers
    • ANTMAN, S.S., KOCH, H.: Self-sustained oscillations of nonlinearly viscoelastic layers. SIAM J. Appl. Math. 60, 1357-1387 (2000)
    • (2000) SIAM J. Appl. Math. , vol.60 , pp. 1357-1387
    • Antman, S.S.1    Koch, H.2
  • 10
    • 0032167181 scopus 로고    scopus 로고
    • The complicated dynamics of heavy rigid bodies attached to light deformable rods
    • ANTMAN, S.S., MARLOW, R.S., VLAHACOS, C.P.: The complicated dynamics of heavy rigid bodies attached to light deformable rods. Quart. Appl. Math. 56, 431-460 (1998)
    • (1998) Quart. Appl. Math. , vol.56 , pp. 431-460
    • Antman, S.S.1    Marlow, R.S.2    Vlahacos, C.P.3
  • 11
    • 0038560483 scopus 로고
    • Large shearing motions of nonlinearly viscoelastic slabs
    • ANTMAN, S.S., SEIDMAN, T.I.: Large shearing motions of nonlinearly viscoelastic slabs. Bull. Tech. Univ. Istanbul 47, 41-56 (1994)
    • (1994) Bull. Tech. Univ. Istanbul , vol.47 , pp. 41-56
    • Antman, S.S.1    Seidman, T.I.2
  • 12
    • 0029692967 scopus 로고    scopus 로고
    • Quasilinear hyperbolic-parabolic equations of nonlinear viscoelasticity
    • ANTMAN, S.S., SEIDMAN, T.I.: Quasilinear hyperbolic-parabolic equations of nonlinear viscoelasticity. J. Diff. Eqs. 124, 132-185 (1996)
    • (1996) J. Diff. Eqs. , vol.124 , pp. 132-185
    • Antman, S.S.1    Seidman, T.I.2
  • 13
    • 0001323666 scopus 로고
    • Un théorème de compacité
    • AUBIN, J.P.: Un théorème de compacité. C. R. Acad. Sci., Paris 265, 5042-5045 (1963)
    • (1963) C. R. Acad. Sci., Paris , vol.265 , pp. 5042-5045
    • Aubin, J.P.1
  • 16
    • 12444319916 scopus 로고
    • The dynamic behavior of viscoelastic spherical shells
    • CALDERER, M.C.: The dynamic behavior of viscoelastic spherical shells. J. Diff. Eqs. 63, 289-305 (1986)
    • (1986) J. Diff. Eqs. , vol.63 , pp. 289-305
    • Calderer, M.C.1
  • 18
    • 0002097881 scopus 로고
    • The mixed initial-boundary value problem for the equations of nonlinear 1-dimensional viscoelasticity
    • DAFERMOS, C.M.: The mixed initial-boundary value problem for the equations of nonlinear 1-dimensional viscoelasticity. J. Diff. Eqs. 6, 71-86 (1969)
    • (1969) J. Diff. Eqs. , vol.6 , pp. 71-86
    • Dafermos, C.M.1
  • 19
    • 0001271072 scopus 로고
    • Global smooth solutions to the initial-boundary-value problem for the equations of one-dimensional nonlinear thermoviscoelasticity
    • DAFERMOS, C.M.: Global smooth solutions to the initial-boundary-value problem for the equations of one-dimensional nonlinear thermoviscoelasticity. SIAM J. Math. Anal. 13, 397-408 (1982)
    • (1982) SIAM J. Math. Anal. , vol.13 , pp. 397-408
    • Dafermos, C.M.1
  • 20
    • 0033329753 scopus 로고    scopus 로고
    • A space-time finite element method for a class of nonlinear hyperbolic-parabolic equations
    • FRENCH, D.A., JENSEN, S., SEIDMAN, T.I.: A space-time finite element method for a class of nonlinear hyperbolic-parabolic equations. Appl. Num. Math. 31, 429-450 (1999)
    • (1999) Appl. Num. Math. , vol.31 , pp. 429-450
    • French, D.A.1    Jensen, S.2    Seidman, T.I.3
  • 21
    • 0020913387 scopus 로고
    • The viscosity-capillarity admissibility criterion for shocks and phase transitions
    • HAGAN, R., SLEMROD, M.: The viscosity-capillarity admissibility criterion for shocks and phase transitions. Arch. Rational Mech. Anal. 83, 333-361 (1983)
    • (1983) Arch. Rational Mech. Anal. , vol.83 , pp. 333-361
    • Hagan, R.1    Slemrod, M.2
  • 22
    • 0000416468 scopus 로고
    • On a model system of equations of one-dimensional gas motion
    • KANEL', YA. I.: On a model system of equations of one-dimensional gas motion (in Russian). Diff. Urav. 4, 721-734 (1969); English translation: Diff. Eqs. 4, 374-380 (1969)
    • (1969) Diff. Urav. , vol.4 , pp. 721-734
    • Kanel, Ya.I.1
  • 23
    • 0000416467 scopus 로고
    • English translation
    • KANEL', YA. I.: On a model system of equations of one-dimensional gas motion (in Russian). Diff. Urav. 4, 721-734 (1969); English translation: Diff. Eqs. 4, 374-380 (1969)
    • (1969) Diff. Eqs. , vol.4 , pp. 374-380
  • 24
    • 0034555717 scopus 로고    scopus 로고
    • Stability and Hopf bifurcation for fully nonlinear parabolic-hyperbolic equations
    • KOCH, H., ANTMAN, S.S.: Stability and Hopf bifurcation for fully nonlinear parabolic-hyperbolic equations. SIAM J. Math. Anal. 32, 360-384 (2001)
    • (2001) SIAM J. Math. Anal. , vol.32 , pp. 360-384
    • Koch, H.1    Antman, S.S.2
  • 26
    • 0009957240 scopus 로고    scopus 로고
    • Mathematical models of liquid crystals
    • LESLIE, F.M., STEWART, I.W. (eds): Mathematical models of liquid crystals. Euro. J. Appl. Math. 8, 251-310 (1997)
    • (1997) Euro. J. Appl. Math. , vol.8 , pp. 251-310
    • Leslie, F.M.1    Stewart, I.W.2
  • 29
    • 0023170272 scopus 로고
    • Phase transitions in one-dimensional nonlinear viscoelasticity: Admissibility and stability
    • PEGO, R.L.: Phase transitions in one-dimensional nonlinear viscoelasticity: Admissibility and stability. Arch. Rational Mech. Anal. 97, 353-394 (1987)
    • (1987) Arch. Rational Mech. Anal. , vol.97 , pp. 353-394
    • Pego, R.L.1
  • 30
    • 0000014325 scopus 로고
    • The transient semiconductor problem with generation terms, II
    • T. E. GILL, W. W. ZACHARY (eds), Springer Lect. Notes Math.
    • SEIDMAN, T.I.: The transient semiconductor problem with generation terms, II. In: Nonlinear Semigroups, Partial Differential Equations, and Attractors. T. E. GILL, W. W. ZACHARY (eds), 1394 Springer Lect. Notes Math. 1989, pp. 185-198
    • (1989) Nonlinear Semigroups, Partial Differential Equations, and Attractors , vol.1394 , pp. 185-198
    • Seidman, T.I.1
  • 31
    • 4544287934 scopus 로고    scopus 로고
    • Optimal control of a nonlinearly viscoelastic rod
    • G. CHEN, I. LASIECKA, J. ZHOU (eds), Marcel Dekker
    • SEIDMAN, T.I., ANTMAN, S.S.: Optimal control of a nonlinearly viscoelastic rod. In: Control of Nonlinear Distributed Parameter Systems. G. CHEN, I. LASIECKA, J. ZHOU (eds), Marcel Dekker, 2001, pp. 273-283
    • (2001) Control of Nonlinear Distributed Parameter Systems , pp. 273-283
    • Seidman, T.I.1    Antman, S.S.2
  • 33
    • 0024130027 scopus 로고
    • Equilibrium states of an elastic conducting rod in a magnetic field
    • SEIDMAN, T.I., WOLFE, P.: Equilibrium states of an elastic conducting rod in a magnetic field. Arch. Rational Mech. Anal. 102, 307-329 (1988)
    • (1988) Arch. Rational Mech. Anal. , vol.102 , pp. 307-329
    • Seidman, T.I.1    Wolfe, P.2
  • 34
    • 0023964748 scopus 로고
    • On the dynamics in space of rods undergoing large motions - A geometrically exact approach
    • SIMO, LC., VU-QUOC, L.: On the dynamics in space of rods undergoing large motions - A geometrically exact approach. Comp. Meths. Appl. Mech. Engg. 66, 125-161 (1988)
    • (1988) Comp. Meths. Appl. Mech. Engg. , vol.66 , pp. 125-161
    • Simo, L.C.1    Vu-Quoc, L.2
  • 36
    • 0346133293 scopus 로고
    • Dynamics of first order phase transitions
    • M. E. GURTIN(ed), Academic Pr.
    • SLEMROD, M.: Dynamics of first order phase transitions, Phase Transformations and Instabilities in Solids. M. E. GURTIN(ed), Academic Pr., 1984, 163-203
    • (1984) Phase Transformations and Instabilities in Solids. , pp. 163-203
    • Slemrod, M.1
  • 37
    • 0034408866 scopus 로고    scopus 로고
    • Unique global solvability for initial-boundary-value problems in one-dimensional nonlinear thermoviscoelasticity
    • WATSON, S.: Unique global solvability for initial-boundary-value problems in one-dimensional nonlinear thermoviscoelasticity. Arch. Rational Mech. Anal. 153, 1-37 (2000)
    • (2000) Arch. Rational Mech. Anal. , vol.153 , pp. 1-37
    • Watson, S.1
  • 39
    • 0036075115 scopus 로고    scopus 로고
    • The motion of a particle on a light viscoelastic bar: Asymptotic analysis of the quasilinear parabolic-hyperbolic equation
    • YIP, S.C., ANTMAN, S.S., WIEGNER, M.: The motion of a particle on a light viscoelastic bar: Asymptotic analysis of the quasilinear parabolic-hyperbolic equation. J. Math. Pures Appl. 81, 283-309 (2002)
    • (2002) J. Math. Pures Appl. , vol.81 , pp. 283-309
    • Yip, S.C.1    Antman, S.S.2    Wiegner, M.3
  • 43
    • 0000967815 scopus 로고
    • The derivation of constitutive relations from the free energy and the dissipative function
    • T. Y. WU, J. W. HUTCHINSON (eds), Academic Press
    • ZIEGLER, H., WEHRLI, C.: The derivation of constitutive relations from the free energy and the dissipative function. In: Advances in Applied Mechanics, vol. 25, T. Y. WU, J. W. HUTCHINSON (eds), Academic Press, 1987, pp. 183-238
    • (1987) Advances in Applied Mechanics , vol.25 , pp. 183-238
    • Ziegler, H.1    Wehrli, C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.