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

Pages: 473 - 492, Volume 8, Issue 2, September 2007

doi:10.3934/dcdsb.2007.8.473       Abstract        Full Text (279.4K)       Related Articles

Guillaume Bal - Department of Applied Physics and Applied Mathematics, Columbia University, New York NY, 10027, United States (email)

Abstract: 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:  Homogenization, random media, high frequency waves.
Mathematics Subject Classification:  Primary: 58F15, 58F17; Secondary: 53C35.

Received: October 2006;      Revised: March 2007;      Published: June 2007.