Some problems in acoustics of emulsions

被引：0
作者：
Gavrikov A.A. [1 ]
Shamaev A.S. [2 ]
机构：
[1] Ishlinskii Institute for Problems of Mechanics, Russian Academy of Sciences, Moscow
[2] Moscow State University, Moscow
来源：
Journal of Mathematical Sciences | 2011年 / 179卷 / 3期
基金：
俄罗斯基础研究基金会;
关键词：
Elastic Material; Homogenize Problem; Complex Part; Convolution Kernel; Spectral Structure;
D O I：
10.1007/s10958-011-0601-6
中图分类号：
学科分类号：
摘要：
The authors study small vibrations of a mixture (emulsion) of two weakly viscous compressible fluids, construct a macroscopic (homogenized) model of emulsion, and establish convergence (with respect to a small parameter) of solutions of the original boundary value problem for a two-phase fluid to solutions of the corresponding homogenized problem. The paper also describes the results of qualitative analysis of the spectrum of the macroscopic acoustic equation (the dynamical Darcy's law), as well as typical spectral pictures obtained by numerical experiments. © 2011 Springer Science+Business Media, Inc.
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页码：415 / 436
页数：21
相关论文
共 35 条
  • [1] Bakhvalov N.S., Panasenko G.P., Averaging of Processes in Periodic Media, (1984)
  • [2] Jikov V.V., Kozlov S.M., Oleinik O.A., Homogenization of Differential Operators and Integral Functionals, (1993)
  • [3] Oleinik O.A., Yosifian G.A., Shamaev A.S., Mathematical Problems in Elasticity and Homogenization, (1992)
  • [4] Pyatnitskii A.L., Chechkin G.A., Shamaev A.S., Homogenization. Methods and Applications, (2007)
  • [5] Sanchez-Palensia E., Nonhomogeneous Media and Vibration Theory, (1984)
  • [6] Frenkel Y.I., On the theory of seismic and seismoelectric phenomena in humid soil, Izv. Akad. Nauk SSSR, Ser. Geography Geophysics, (1944)
  • [7] Biot M.A., Generalized theory of acoustic propagation in porous dissipative media, J. Acoust. Soc. Amer., 34, pp. 1254-1264, (1962)
  • [8] Gilbert R.P., Mikelic A., Homogenizing the acoustic properties of the seabed", Pt. I, Nonlinear Anal., 40, pp. 185-212, (2000)
  • [9] Nguetseng G., A general convergence result for a functional related to the theory of homogenization, SIAM J. Math. Anal., 20, 3, pp. 608-623, (1989)
  • [10] Nguetseng G., Asymptotic analysis for a staff variational problem arising in mathematics, SIAM J. Math. Anal., 21, 6, pp. 1396-1414, (1990)
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