Abstract
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).
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References
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)
N.S. BAKHVALOV and G.P PANASENKO, Homogenization: Averaging Processes in Periodic Media Kluwer Ac. Publ., Dordrecht/London/ Boston, 1989.
A.L. PIATNITSKY, Refraction problem for a stratified medium, Math. USSR Sbornik, 115, No 3, 1981.
V. BERDICHEVSKY and V. SUTYRIN, The dynamics of periodic structures, Soviet Phys. Doklady, 28, No 3, 1983, pp. 239–241.
Y. AMIRAT, K. HAMDACHE, A. ZIANI, Homogénisation d’un modèle d’écoulements miscibles en milieu poreux, Asymptotic Analysis, 3, 1990, pp. 77–89.
A. BOURGEAT, A. MIKELIC, Homogenization of two-phase immiscible flows in a one-dimensional porous medium, Asymptotic Analysis, 9, 1994, pp. 359–380.
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.
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Lapshin, E.A., Panasenko, G.P. (2000). Homogenization of the System Equations of High Frequency Nonlinear Acoustics. In: Gilbert, R.P., Kajiwara, J., Xu, Y.S. (eds) Direct and Inverse Problems of Mathematical Physics. International Society for Analysis, Applications and Computation, vol 5. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3214-6_13
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DOI: https://doi.org/10.1007/978-1-4757-3214-6_13
Publisher Name: Springer, Boston, MA
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