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.

翻译：对于某些空间上非局部扩散模型,其非局部互动范围有限,以正参数 $\delta$衡量,我们审查在与某些不相容的数据相对应的各种条件下界定的封闭域域的配方。我们认为,这些配方与传统局部差异方程(PDE)模型的相似异同边界值问题是一致的,因为非本地互动内核以当地$=delta\ to 0$的限值本地化,同时,对于重新标定的片型内核,与全球$\delta\\to\infty$限制的分方程式的异异异非本地边界值问题相对应。这种讨论有助于用不相容数据界定与封闭域界定的非本地问题有关的问题。