Axisymmetric fundamental solutions for the equations of heat conduction in the case of cylindrical anisotropy of a medium

Abstract

Numerical methods of solving the boundary-value problems for the equations of mathematical physics based on the application of fundamental solutions, i.e., solutions describing the reaction of infinite space or an infinite plane to a concentrated action, are currently in widespread favor. Among these methods we can include the direct and indirect methods of boundary integral equations [i], as well as the method of sources in which the solution of the boundary-value problem is constructed by superposition of concentrated actions in space, above some surface encompassing the area under investigation [2]. For the equations of steady and nonsteady heat conduction in an isotropic medium such solutions are well established (see [i] and the references cited there) both for the twoand three-dimensional cases, as well as for the case of the axisymmetric problem. The plane and three-dimensional equations of heat conduction for a rectilinear anisotropic medium can be reduced to the isotropic case. We know of three-dimensional fundamental solutions for the equations of elasticity theory in the case of a medium with rectilinear anisotropy [3] and for a rectilinear anisotropic hereditary (or memory) elastic medium [4, 5].