Solution of Boundary Value Problems for Laplace's Equationin a Piecewise Homogeneous Planewith a Parabolic Crack (Screen)

摘要

Boundary value problems for Laplace's equation are considered in a piecewise homoge-neous plane divided into two zones by a strongly permeable crack or a weakly permeable screen in theform of a parabola. The desired potentials have prescribed singular points (sources, sinks, etc.). For-mulas are derived expressing the potentials in terms of harmonic functions that have the given singularpoints and describe similar processes in a homogeneous plane.