The deduction of the homogenized model of isothermal acoustics in a heterogeneous medium in the case of two different poroelastic domains

We consider a mathematical model of isothermal acoustics in a composite medium consisting of two different porous soils (poroelastic domains) with common boundary. Each of the domains has its own characteristics of the solid skeleton; the fluid filling the pores is the same for both domains. The differential equations of the accurate model contain rapidly oscillating coefficients. We deduce homogenized equations (i.e. equations not containing rapidly oscillating coefficients).