Properties of Averaged Models of the Periodic Media Mechanics

  • Nickolaj S. Bakhvalov
  • Margarita E. Eglit
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 5)


In homogenization of processes (or stationary states) in periodic structures the equations of other types comparing to original ones often arise. In this work we discuss briefly some of such situations. In particular we consider the problem of conservation of variational properties of a model in homogenization.


Sound Velocity Periodic Structure Average Model Periodic Medium Perturbation Velocity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    N. Bakhvalov, “On the sound velocity in mixtures”, DAN„SSSR, 245 (1979), 1345–1348, (in Russian).MathSciNetGoogle Scholar
  2. [2]
    N. Bakhvalov, “Homogenization and perturbation problems”, Computing Methods in Aplied Science and Engineering, Amsterdam, North Holland, 1980, 645–658.Google Scholar
  3. [3]
    N. Bakhvalov, M. Eglit, “Processes in periodic media which could not be described in terms of averaged characteristics”, DAN SSSR, 268(1983), 836–840, (in Russian).MathSciNetGoogle Scholar
  4. [4]
    N. Bakhvalov, M. Eglit, “Variational properties of averaged equations of periodic media”, Trudy MIAN, Moscow, 192 (1990), 5–19, (in Russian).MathSciNetGoogle Scholar
  5. [5]
    N. Bakhvalov, G. Panasenko, “Homogenization: averaging processes in periodic media”, Mathematical Problems in the Mechanics of Composite Materials, Kluwer Academic Publishers, Dordrecht-Boston-London, 1989.CrossRefGoogle Scholar
  6. [6]
    M. Eglit, “On the averaged description of the processes in periodic elastic-plastic media”, MKM, Riga, 5 (1984), 825–831, (in Russian).Google Scholar
  7. [7]
    M. Eglit, “On averaged description of large-scale processes in periodic viscous compressable media”, Mechanics. Current Problems, MGU, Moscow, 1987, 121–126, (in Russian).Google Scholar
  8. [8]
    J. L. Lions, “Some methods in the mathematical analysis of systems and their control”, Science Press, Beijing, China, 1981.Google Scholar
  9. [9]
    S. Mozolin, “About nearness of solutions of original and averaged problems of electrodynamics and visco-elasticity”, DAN SSSR, 273 (1983), 330–333, (in Russian).MathSciNetGoogle Scholar
  10. [10]
    E. Sanches-Palencia, “Non-homogenious media and vibration theory”, Lecture Notes in Physics, 127, Berlin, Springer-Verlag, 1980.Google Scholar

Copyright information

© Birkhäuser Boston 1991

Authors and Affiliations

  • Nickolaj S. Bakhvalov
    • 1
  • Margarita E. Eglit
    • 2
  1. 1.Dept. of Numerical MathematicsUSSR Academy of SciencesMoscowUSSR
  2. 2.Dept. of Mathematics and MechanicsMoscow State Univ.MoscowUSSR

Personalised recommendations