Seminar in Mathematical Modeling and Analysis - Pedro Hernandez

The seminars in Mathematical Modeling and Analysis are aimed at researchers, employees, and students.

This week's seminar is given by Pedro Hernandez, Universidad de O'Higgins.

Title: Poroelastic plate model obtained by simultaneous homogenization and dimension reduction

Abstract: In this talk, the starting point of our analysis is coupled system of elasticity and weakly compressible fluid. We consider two small parameters: the thickness $h$ of the thin plate and the pore scale $\varepsilon_h$ which depend on $h$. We will focus specifically on the case when the pore size is small relative to the thickness of the plate. The main goal here is derive a model for a poroelastic plate 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 in ``A. Marcianiak-Czochra, A. Mikeli\'c, A rigorous derivation of the equations for the clamped Biot-Kirchhoff-Love poroelastic plate, Arch. Rational Mech. Anal. 215 (2015), 1035-1062'' by dimension reduction techniques from $3D$ Biot's equations. This is a joint work with I. Vel\v ci\'c,  J. \v Zubrini\'c and M. Bu\v zan\v ci\'c.