论文标题
具有一致局部和分数限制的非局部扩散模型
Nonlocal diffusion models with consistent local and fractional limits
论文作者
论文摘要
对于某些在空间非局部扩散模型中具有有限的非局部相互作用范围的非局部相互作用的范围，我们审查了它们在符合各种条件的有界域上定义的公式，这与某些不均匀数据相对应。我们认为它们对经典部分偏微分方程（PDE）模型的类似不均匀边界价值问题的一致性，因为非局部相互作用内核在本地$δ\ 0 $限制中本地化，同时，对于重新固定的分数型内核，与相应的非元素边界值$ $ $ $ $ $ $ $ $ $ $ nimim fracty $ unfacty $ unfacty $ unfacty $ nimim of fractimation $。此类讨论有助于描述与有限域中定义的非均匀数据定义的非本地问题有关的问题。
For some spatially nonlocal diffusion models with a finite range of nonlocal interactions measured by a positive parameter $δ$, 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 $δ\to 0$ limit, and at the same time, for rescaled fractional type kernels, to corresponding inhomogeneous nonlocal boundary value problems of fractional equations in the global $δ\to \infty$ limit. Such discussions help to delineate issues related to nonlocal problems defined on a bounded domain with inhomogeneous data.
