J. Badur, Sun Bohua. Remarks on the Structure of Evolution Equations[J]. Applied Mathematics and Mechanics, 1995, 16(8): 699-707.
Citation: J. Badur, Sun Bohua. Remarks on the Structure of Evolution Equations[J]. Applied Mathematics and Mechanics, 1995, 16(8): 699-707.

Remarks on the Structure of Evolution Equations

  • Received Date: 1994-08-16
  • Publish Date: 1995-08-15
  • In the paper the evolution equations are discussed so as to enable a phenomenological description of microstruchtral behaviour e.g. partially reversible flow of Maxwellian gas, recovery structural relaxation and other experimental results coming from light scattering and molecular dynamics.The result deals with the revaluation of Zaremba's ansatz.It leads to resolution of problems with substantial and available nonlinearities in the transport equation.
  • loading
  • [1]
    L. G. Colin, Extended non-equilibrium thermodynamics, scope and limitations, Revista Mex. Fisica, 34(1988), 344-366.
    [2]
    Z.H. Guo, Time derivatives of tensor fields in nonlinear continuum mechanics, Arch. Mech. Stosow, 15(1963), 131-163.
    [3]
    Maria Heckl and I. Müller, Frame dependence, entropy, entropy flux, and wave speeds in mixtures of gases, Acta Mech., 50(1983), 71-95.
    [4]
    D. Jou, J. Cassas-Vazquez and G. Lebon, Extended irreversible thermodynamics, Rep. Ping. Plps., 51(1988), 1105-1179.
    [5]
    J. Kestin, A note on the relation between the hypothesis of local equilibrium and the Clausius-Duhem inequality, J. Non-Eguilib. Thernrodvrr., 18(1990), 193-212.
    [6]
    J. Kestin, Local-equilibrium formalism applied to mechanics of solids. Int. J. Solids. Strue., 29(1992), 1827-1836.
    [7]
    J. Kestin, Thermodynamics (an essey) in: Zagadnienia Maszyn Przelpyuouych, Proc, of Conf on 90th Aniversary of Robert Szewalski, ed, S. Burka Gdansk(1993),,319-334.
    [8]
    I.-L. Liu and I. Müller, on the thermodynamics and thermostatics of fluids in electromagnetic field, Arch. Rutiorral Meclr. Anal., 46(1972), 149-176.
    [9]
    I.-L. Liu, On thermodynamics of viscoelasticity, in: Proc. 2nd Int. Conf. Nonlinear Mech., Beijing, ed. Z. H. Guo(1993), 174-177.
    [10]
    G. A. Maugin and C. Trimarco, Pseudomomentum and material forces in nonlinear elasticity: variational formmulations and application to brittle fructure, Acta Mech., 94 (1992), 1-28.
    [11]
    I. Müller, Zum Paradoxon der Wärmeleitungstheorie, Z. für Physik, 198(1967), 329-344
    [12]
    I. Müller and K. Wilmanski, Extended thermodynamics of a non-Newtonian fluid, Rheo. Acta, 25(1986), 335-349.
    [13]
    I. Müller, On the frame dependence of stress and heat flux, Arch. Rational Mech. Anal., 45(1972), 241-250
    [14]
    I. Müller, The structure of extended thermodynamics, in Trends in Applications of Mathematics to Mechanics, eds. W. Schneider, H. Troger, F. Zigler, Longman Sci.& Tech.(1992), 164-173.
    [15]
    I. Müller and T. Ruggeri, Extended thermodynamics, in Spriuger Tracts Natur. Phil., ed. C. Truesdell, 37(1993)
    [16]
    L. Natanson, Sur les lois de la diffusion, Bull. lnt. l'Acad. Sci. Letters. Cracovie (A) (1901),335-348.
    [17]
    L. Restuccia and B. Maruszewski, Diffusion and dislocation influence on the dynamics of elastic bodies, Int. J. Engn. Sci., 29(1991).1053-1063.
    [18]
    H. Stumpf and J. Badur. On missine links of rate-independent elastoplasticitv at finite strain, Mech. Res. Comm., 17, 5 (1990), 353-364.
    [19]
    H. Stumpf and J. Badur, On a generalization of elasto-plastic models within the frame of extended thermodynamics, ZAMM, 72 (1993), T211-214.
    [20]
    H. Stumpf and J. Badur, On surface objective rates, Quart. Appl. Math., 51 (1993),161-186.
    [21]
    B.H. dun, A simple review of elasto-plastic models, CERECAM Report No. 252, University of-Cape Town South Africa(1994), 1-55.
    [22]
    B.H. Sun and J. Badur, Some remarks on the multiplicative ecomposition within elasto-plasticity.
    [23]
    C. Truesdell and R. Toupin, The classical field theories, Hand. der Phys., Bd III/I, ed. S.Fllüge (1960), 226-793. (appendix by J. L. Ericksen, 794-858).
    [24]
    K. Wilmanski, Thermodynamics of a heat conducting Maxwellian fluid, Arch, Mech. Stosow, 40 (1988), 217-232.
    [25]
    S. Zaremna, Sur une forme perfectionee de la theorie de la relaxation, Bull. Int. I'Acad.Sci. Lettres Cracovie (CI. Sci. Math. Natur.) A (1903), 594-614.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1599) PDF downloads(476) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return