We investigate the behavior of the solution of a mixed problem in a domain with two moderately close holes. We introduce a positive parameter ε and we define a perforated domain Ωε obtained by making two small perforations in an open set. Both the size and the distance of the cavities tend to 0 as ε → 0. For ε small, we denote by uε the solution of a mixed problem for the Laplace equation in Ωε. We describe what happens to uε as ε → 0 in terms of real analytic maps and we compute an asymptotic expansion.
A mixed problem for the Laplace operator in a domain with moderately close holes
Musolino P.
2016
Abstract
We investigate the behavior of the solution of a mixed problem in a domain with two moderately close holes. We introduce a positive parameter ε and we define a perforated domain Ωε obtained by making two small perforations in an open set. Both the size and the distance of the cavities tend to 0 as ε → 0. For ε small, we denote by uε the solution of a mixed problem for the Laplace equation in Ωε. We describe what happens to uε as ε → 0 in terms of real analytic maps and we compute an asymptotic expansion.
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