Homogenization of the acoustic equations for a porous long-memory viscoelastic material filled with a viscous fluid

Homogenization of Equations of Dynamics of a Medium Consisting of Viscoelastic Material with Memory and Incompressible Kelvin–Voigt Fluid

“…Then we apply the Laplace transform in time t to (1.4)-(1.6) and denote by g λ or g(λ), the image of g(t), where λ is the Laplace transform parameter. Arguing as in [4]- [6], one can show that…”

“…We find explicit analytic expressions for coefficients and convolution kernels of the homogenized equations corresponding to the case of a layered medium. Bibliography: 12 titles.Homogenization of the equations of dynamics of a periodic two-phase medium consisting of a solid (elastic or viscoelastic) material and a viscous Newton fluid was studied, for example, in [1]- [6]. According to the results of the cited works, the homogenized equations are partial and integro-differential equations of the third order.…”

“…Homogenization of the equations of dynamics of a periodic two-phase medium consisting of a solid (elastic or viscoelastic) material and a viscous Newton fluid was studied, for example, in [1]- [6]. According to the results of the cited works, the homogenized equations are partial and integro-differential equations of the third order.…”

Homogenization of Acoustic Equations for a Partially Perforated Elastic Material with Slightly Viscous Fluid

“…In applications, such problems describe some physical processes in heterogeneous media, for example, a diffusion process in highly heterogeneous media [2] or a joint motion of an elastic skeleton and a slightly viscous fluid [7]. Recently, the method of two-scale convergence is widely applied in the homogenization of various mathematical problems that arise in mechanics of heterogeneous media (see, e.g., [8][9][10][11][12][13][14]). …”