Systems of Functions Consistent with Inhomogeneities of Elliptic and Spheroidal Shapes in Problems of Continuum Mechanics

Abstract

Structure of the fundamental solutions of the Laplace equation in the elliptic and spheroidal coordinate systems is investigated. It was shown that among the solutions separated in these coordinate systems there are such solutions that have the form of harmonic polynomials in the original Cartesian coordinate system. These polynomials constitute basis for constructing with the help of radial multipliers the fundamental systems of functions that are consistent with the inhomogeneities of the elliptic and ellipsoidal shapes. These functions are used in problems of mechanics of inhomogeneous media for accurate modeling of physical processes near such inclusions. On the basis of these functions algorithms are constructed for defining effective thermophysical characteristics of inhomogeneous media with inclusions of elliptic and spheroidal shapes.