2009•Computational Mathematics and Mathematical PhysicsRequires access

Solution of boundary value problems for Laplace’s equation in a piecewise homogeneous plane with a parabolic crack (screen)

С. Е. Холодовский

Abstract

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

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Key concepts: Mathematics, Mathematical analysis, Laplace transform, Piecewise, Homogeneous, Laplace's equation, Boundary value problem, Plane (geometry)