Date/heure
15 novembre 2019
11:00 - 12:00
Oratrice ou orateur
Malte PETER
Catégorie d'évènement Séminaire EDP, Analyse et Applications (Metz)
Résumé
Reaction-diffusion processes occur in many materials with microstructure such as biological cells, steel or concrete. The main difficulty in modelling and simulating accurately such processes is to account for the fine microstructure of the material. One method of upscaling multiscale problems, which has proven reliable for obtaining feasible macroscopic models rigorously, is the method of periodic homogenisation. The correct scaling of certain terms of the system with powers of the homogenisation parameter is an aspect particularly relevant in this context. The scaling arises from geometrical considerations or from the processes themselves. Depending on the particular choice of these scaling powers, different limit behaviours are obtained leading to different systems of equations in the homogenisation limit. This will first be discussed in the context of a reaction-diffusion system given in a two-component medium coupled by a Robin condition at the internal interface. The analogous vector-valued problem models two elastic materials coupled by a slip-displacement condition, which will be the focus of the second part of the talk.