The Dirichlet problem in a planar domain with two moderately close holes

Matteo Dalla Riva, Paolo Musolino

Allbwn ymchwil: Cyfraniad at gyfnodolynErthygladolygiad gan gymheiriaid

5 Dyfyniadau (Scopus)
170 Wedi eu Llwytho i Lawr (Pure)

Crynodeb

We investigate a Dirichlet problem for the Laplace equation in a domain of R2 with two small close holes. The domain is obtained by making in a bounded open set two perforations at distance |ϵ1| one from the other and each one of size |ϵ1ϵ2|. In such a domain, we introduce a Dirichlet problem and we denote by uϵ1,ϵ2 its solution. We show that the dependence of uϵ1,ϵ2 upon (ϵ1,ϵ2) can be described in terms of real analytic maps of the pair (ϵ1,ϵ2) defined in an open neighbourhood of (0,0) and of logarithmic functions of ϵ1 and ϵ2. Then we study the asymptotic behaviour of uϵ1,ϵ2 as ϵ1 and ϵ2 tend to zero. We show that the first two terms of an asymptotic approximation can be computed only if we introduce a suitable relation between ϵ1 and ϵ2.
Iaith wreiddiolSaesneg
Tudalennau (o-i)2567-2605
Nifer y tudalennau39
CyfnodolynJournal of Differential Equations
Cyfrol263
Rhif cyhoeddi5
Dyddiad ar-lein cynnar12 Ebr 2017
Dynodwyr Gwrthrych Digidol (DOIs)
StatwsCyhoeddwyd - 05 Medi 2017

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