  A mixed boundary value problem for the partial differential equation of
diffusion in an inhomogeneous medium in a Lipschitz domain is reduced to a
system of direct segregated parametrix-based Boundary-Domain Integral Equations
(BDIEs). We use a parametrix different from the one employed in the papers by
Mikhailov (2002, 2006) and Chkadua, Mikhailov, Natroshvili (2009). We prove the
equivalence between the original BVP and the corresponding BDIE system. The
invertibility and Fredholm properties of the boundary-domain integral operators
are also analysed.
