Degenerate scale for the Laplace problem in the half-plane; Approximate logarithmic capacity for two distant boundaries

Abstract : We study the problem of finding a degenerate scale for Laplace equation in a half-plane. It is shown that if the boundary condition on the line bounding the half-plane is of Dirichlet type, there is no degenerate scale. In the case of a boundary condition of Neumann type, there is a degenerate scale, which is shown to be the same as the one for the symmetrized contour with respect to the boundary line in the full plane. We show next a formula for obtaining the degenerate scale of a domain made of two parts, when the components are far from each other, which allows to obtain the degenerate scale for the symmetrized contour. Finally, we give some examples of evaluation of the degenerate scale both by an approximate formula and by a numeric evaluation using integral methods.These evaluations show that the approximate solution is still valid for small values of the distance between symmetrized contours.
Complete list of metadatas

https://hal-upec-upem.archives-ouvertes.fr/hal-00806771
Contributor : Guy Bonnet <>
Submitted on : Sunday, January 17, 2016 - 12:13:52 PM
Last modification on : Friday, October 4, 2019 - 1:33:50 AM
Long-term archiving on : Monday, April 18, 2016 - 10:04:20 AM

File

article-corfdir-bonnet-eabe-20...
Files produced by the author(s)

Identifiers

Citation

Alain Corfdir, Guy Bonnet. Degenerate scale for the Laplace problem in the half-plane; Approximate logarithmic capacity for two distant boundaries. Engineering Analysis with Boundary Elements, Elsevier, 2013, 37 (5), pp.219-224. ⟨10.1016/j.enganabound.2013.02.009⟩. ⟨hal-00806771⟩

Share

Metrics

Record views

394

Files downloads

283