Date/heure
15 mai 2018
10:45 - 11:45
Oratrice ou orateur
Paolo Musolino
Catégorie d'évènement Séminaire Équations aux Derivées Partielles et Applications (Nancy)
Résumé
In this talk, we present some recent results on the analysis of singular perturbation problems in perforated domains. First, we will consider the asymptotic behavior of the solutions of a mixed problem for the Laplace equation in a domain with moderately close holes, i.e., with distance tending to zero « not faster » than the size. We describe what happens to the solutions in terms of real analytic maps and we compute asymptotic expansions, by an approach based on Potential Theory and Functional Analysis. Then we will show how our method can be exploited to analyze the influence of perforations approaching to a point of the boundary. First we will assume that the boundary is « flat » around the « singular » point. Then we will consider perforations concentrating around the vertex of a planar sector. The talk is based on joint works with V. Bonnaillie-No »el, M. Costabel, M. Dalla Riva, M. Dambrine, and M. Dauge. »