Crynodeb
We consider the Dirichlet problem for the Laplace equation in a planar domain with a small hole. The diameter of the hole is proportional to a real parameter ε and we denote by uε the corresponding solution. If p is a point of the domain, then for ε small we write uε(p) as a convergent power series of ε and of 1/(r0 + (2π)-1 log |ε|), with r0 ∈ ℝ. The coefficients of such series are given in terms of solutions of recursive systems of integral equations. We obtain a simplified expression for the series expansion of uε(p) in the case of a ring domain.
Iaith wreiddiol | Saesneg |
---|---|
Tudalennau (o-i) | 339-361 |
Nifer y tudalennau | 23 |
Cyfnodolyn | Asymptotic Analysis |
Cyfrol | 92 |
Rhif cyhoeddi | 3-4 |
Dynodwyr Gwrthrych Digidol (DOIs) | |
Statws | Cyhoeddwyd - 2015 |