Homogenization in random media and effective medium theory for high frequency waves

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September 2007, 8(2): 473-492. doi: 10.3934/dcdsb.2007.8.473

Homogenization in random media and effective medium theory for high frequency waves

1.	Department of Applied Physics and Applied Mathematics, Columbia University, New York NY, 10027

Received October 2006 Revised March 2007 Published June 2007

Abstract
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We consider the homogenization of the wave equation with high frequency initial conditions propagating in a medium with highly oscillatory random coefficients. By appropriate mixing assumptions on the random medium, we obtain an error estimate between the exact wave solution and the homogenized wave solution in the energy norm. This allows us to consider the limiting behavior of the energy density of high frequency waves propagating in highly heterogeneous media when the wavelength is much larger than the correlation length in the medium.

Keywords: random media, high frequency waves., Homogenization.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.

Citation: Guillaume Bal. Homogenization in random media and effective medium theory for high frequency waves. Discrete & Continuous Dynamical Systems - B, 2007, 8 (2) : 473-492. doi: 10.3934/dcdsb.2007.8.473

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