Ricerc@Sapienza

This work investigates the capabilities of two different approaches for the analysis of thin-walled structures, both based on
enriched beam theories that include out-of-plane cross-section warping, being the in-plane deformations neglected.

We study the weak solvability of a system of coupled Allen--Cahn--like equations resembling cross--diffusion which is arising as a model for the consolidation of saturated porous media. Besides using energy like estimates, we cast the special structure of the system in the framework of the Leray--Schauder fixed point principle and ensure this way the local existence of strong solutions to a regularised version of our system. Furthermore, weak convergence techniques ensure the existence of weak solutions to the original consolidation problem.