Published Paper

Inserted: 16 jun 2026
Last Updated: 16 jun 2026

Journal: Journal of Evolutions Equations
Volume: 26
Number: 12
Pages: 88
Year: 2026
Doi: https://doi.org/10.1007/s00028-025-01152-z
Links: Springer Link

Abstract:

In this paper, the starting point of our analysis is a coupled system of linear elasticity and Stokes equation. We consider two small parameters: the thickness $h$ of the thin plate and the pore scale $\varepsilon(h)$ that depends on $h$. We will focus specifically on the case when the pore size is comparatively small relative to the thickness of the plate. The main goal here is to derive a model of a poroelastic plate, starting from the 3D problem as $h$ goes to zero, using simultaneous homogenization and dimension reduction techniques. The obtained model generalizes the poroelastic plate model derived by Mikelić et al. (Arch Ration Mech Anal 215:1035–1062, 2015) using dimension reduction techniques from 3D Biot’s equations in the sense that it also covers the case of contacts of poroelastic and (poro)elastic plate as well as the evolution equation with inertial term.

Keywords: Homogenization, dimension reduction, Two-scale convergence, Poroelastic plate