Homogenization of the System Equations of High Frequency Nonlinear Acoustics

  • Evgueny A. Lapshin
  • Gregory P. Panasenko
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 5)


High frequency nonlinear acoustics equations proposed in [1] are considered. The acoustic characteristics of the medium rapidly oscillate. This model describes the propagation of pulses of sound shocks generated by supersonic planes, blast waves in atmosphere and ocean, continuous radiation of sound sources. An asymptotic solutions of high frequency nonlinear acoustics equations is constructed (when the characteristic size of inhomogeneity is small with respect to the height of the layer where the problem is posed).


Asymptotic Solution Effective Medium Blast Wave Eikonal Equation Contraction Operator 
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  1. [1]
    O.V. RUDENKO, A.K. SUKHORUKOVA and A.P. SUKHORUKOV, Equations of high frequency nonlinear acoustics of heterogeneous media Acoustic Journal, 40, No 2, 1994 (in Russian)Google Scholar
  2. [2]
    N.S. BAKHVALOV and G.P PANASENKO, Homogenization: Averaging Processes in Periodic Media Kluwer Ac. Publ., Dordrecht/London/ Boston, 1989.Google Scholar
  3. [3]
    A.L. PIATNITSKY, Refraction problem for a stratified medium, Math. USSR Sbornik, 115, No 3, 1981.Google Scholar
  4. [4]
    V. BERDICHEVSKY and V. SUTYRIN, The dynamics of periodic structures, Soviet Phys. Doklady, 28, No 3, 1983, pp. 239–241.Google Scholar
  5. [5]
    Y. AMIRAT, K. HAMDACHE, A. ZIANI, Homogénisation d’un modèle d’écoulements miscibles en milieu poreux, Asymptotic Analysis, 3, 1990, pp. 77–89.MathSciNetzbMATHGoogle Scholar
  6. [6]
    A. BOURGEAT, A. MIKELIC, Homogenization of two-phase immiscible flows in a one-dimensional porous medium, Asymptotic Analysis, 9, 1994, pp. 359–380.MathSciNetzbMATHGoogle Scholar
  7. [7]
    E.A.LAPSHIN, G.P.PANASENKO, Homogenization of the equations of high frequency nonlinear acoustics, C.R.Acad.Sci.Paris, 325, serie 1, 1997, pp. 931–936.MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Evgueny A. Lapshin
    • 1
    • 2
  • Gregory P. Panasenko
    • 2
  1. 1.Math. — Mech. DepartmentMoscow State UniversityMoscowRussia
  2. 2.CNRS UMR 5585, Equipe d’Analyse NumériqueUniversité Jean MonnetSaint-Etienne CedexFrance

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