  For some spatially nonlocal diffusion models with a finite range of nonlocal
interactions measured by a positive parameter $\delta$, we review their
formulation defined on a bounded domain subject to various conditions that
correspond to some inhomogeneous data. We consider their consistency to similar
inhomogeneous boundary value problems of classical partial differential
equation (PDE) models as the nonlocal interaction kernel gets localized in the
local $\delta\to 0$ limit, and at the same time, for rescaled fractional type
kernels, to corresponding inhomogeneous nonlocal boundary value problems of
fractional equations in the global $\delta\to \infty$ limit. Such discussions
help to delineate issues related to nonlocal problems defined on a bounded
domain with inhomogeneous data.
