An R-linear conjugation problem for a plane two-component heterogeneous structure with an array of periodically distributed sinks/sources

An R-linear conjugation problem for a planar structure consisting of an isotropic strip and adjacent half-plane with contrasting permeabilities is solved. The whole structure is bounded from above by an equipotential line. An exact analytical solution is derived in terms of complex velocity in the class of one-periodical piece-wise meromorphic functions. Their principal part is the sum of periodically distributed simple poles, fixed in advance. Cases with singularities internal to the strip and subjacent half-plane are distinguished from a special case of poles positioned along the interface.