Details

Autor(en) / Beteiligte

• Mityushev, Vladimir
• Rogosin, Sergei
• Drygaś, Piotr

Titel

Mixed Problem for Laplace's Equation in an Arbitrary Circular Multiply Connected Domain

Ist Teil von

• Modern Problems in Applied Analysis, 2018, p.135-152

Ort / Verlag

Switzerland: Springer International Publishing AG

Erscheinungsjahr

2018

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Mixed boundary value problems for the two-dimensional Laplace’s equation in a domain D are reduced to the Riemann-Hilbert problem Re λ(t)¯ψ(t)=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\overline {\lambda (t)}\psi (t) = 0$$ \end{document}, t ∈ ∂D, with a given Hölder continuous function λ(t) on ∂D except at a finite number of points where a one-sided discontinuity is admitted. The celebrated Keldysh-Sedov formulae were used to solve such a problem for a simply connected domain. In this paper, a method of functional equations is developed to mixed problems for multiply connected domains. For definiteness, we discuss a problem having applications in composites with a discontinuous coefficient λ(t) on one of the boundary components. It is assumed that the domain D is a canonical domain, the lower half-plane with circular holes. A constructive iterative algorithm to obtain an approximate solution in analytical form is developed in the form of an expansion in the radius of the holes.