Homogenization of the acoustic equations for a porous long-memory viscoelastic material filled with a viscous fluid
А. С. Шамаев, Владлена Валерьевна Шумилова · Differential Equations · 2012
We consider the system of linear differential and integro-differential equations describing small vibrations in an ɛ -periodic combined medium consisting of a porous long-memory viscoelastic material and a viscous fluid filling the pores. By using the two-scale convergence method, we construct the system of homogenized equations and prove the convergence of solutions of the original problems to the solution of the homogenized problem as ɛ → 0.