Averaging the acoustics equations for a viscoelastic material with channels filled with a viscous compressible fluid

A mathematical model describing small oscillations of a combined medium consisting of an ɛ-periodic porous viscoelastic material and a viscous compressible fluid filling the pores is considered. For this model an effective averaged model is developed and the convergence of the solutions of prelimiting problems, as ɛ → 0, to the solution of the averaged problem in the L ² space norm is proved.