Global representation and multi-scale expansion for the Dirichlet problem in a domain with a small hole close to the boundary - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2019

Global representation and multi-scale expansion for the Dirichlet problem in a domain with a small hole close to the boundary

Résumé

For each pair ε = (ε 1 , ε 2) of positive parameters, we define a perforated domain Ω ε by making a small hole of size ε 1 ε 2 in an open regular subset Ω of R n (n ≥ 3). The hole is situated at distance ε 1 from the outer boundary ∂Ω of the domain. Then, when ε → (0, 0) both the size of the hole and its distance from ∂Ω tend to zero, but the size shrinks faster than the distance. In such perforated domain Ω ε we consider a Dirichlet problem for the Laplace equation and we denote by u ε its solution. Our aim is to represent the map that takes ε to u ε in term of real analytic functions of ε defined in a neighborhood of (0, 0). In contrast with previous results valid only for restrictions of u ε to suitable subsets of Ω ε , we prove a global representation formula that holds on the whole of Ω ε. Such a formula allows to rigorously justify multi-scale expansions, which we subsequently construct.
Fichier principal
Vignette du fichier
190216_asybdryhole.pdf (440.59 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02176154 , version 1 (07-07-2019)

Identifiants

  • HAL Id : hal-02176154 , version 1

Citer

Virginie Bonnaillie-Noël, Matteo Dalla, Marc Dambrine, Paolo Musolino. Global representation and multi-scale expansion for the Dirichlet problem in a domain with a small hole close to the boundary. 2019. ⟨hal-02176154⟩
82 Consultations
110 Téléchargements

Partager

Gmail Facebook X LinkedIn More