On linking n-dimensional anisotropic and isotropic Green's functions for infinite space, half-space, bimaterial, and multilayer for conduction

We establish exact mathematical links between the n-dimensional anisotropic and isotropic Green's functions for diffusion phenomena for an infinite space, a half-space, a bimaterial and a multilayered space. The purpose of this work is not to attempt to present a solution procedure, but to focus on the general conditions and situations in which the anisotropic physical problems can be directly linked with the Green's functions of a similar configuration with isotropic constituents. We show that, for Green's functions of an infinite and a half-space and for all two-dimensional configurations, the exact correspondences between the anisotropic and isotropic ones can always be established without any regard to the constituent conductivities or any other information. And thus knowing the isotropic Green's functions will readily provide explicit expressions for anisotropic Green's functions upon back transformation. For three- and higher-dimensional bimaterials and layered spaces, the correspondence can also be found but the constituent conductivities need to satisfy further algebraic constraints. When these constraints are fully satisfied, then the anisotropic Green's functions can also be obtained from those of the isotropic ones, or at least in principle.