An ℝ-linear conjugation problem for two concentric annuli

Abstract

We consider an infinite planar four-phase heterogeneous medium with three concentric circles as a boundary between isotropic medium's components of distinct resistivities/conductivities. It is supposed that the velocity field in this structure is generated by a finite set of arbitrary multipoles. We distinguish two cases when multipoles are inside of medium's components or at the interface. An exact analytical solution of the corresponding R-linear conjugation boundary value problem is derived for both cases. Examples of flow nets (isobars and streamlines) are presented.