A rigorous limit procedure is presented which links nonlocal models involving adhesion or nonlocal chemotaxis to their local counterparts featuring haptotaxis and classical chemotaxis, respectively. It relies on a novel reformulation of the involved nonlocalities in terms of integral operators applied directly to the gradients of signal-dependent quantities. The proposed approach handles both model types in a unified way and extends the previous mathematical framework to settings that allow for general solution-dependent coefficient functions. The previous forms of nonlocal operators are compared with the new ones introduced in this paper and the advantages of the latter are highlighted by concrete examples. Numerical simulations in 1D provide an illustration of some of the theoretical findings.

提出了严格的限制程序，该程序将涉及粘附或非局部趋化性的非局部模型与分别具有触觉趋化性和经典趋化性的局部模型联系起来。它依靠直接应用于信号相关量的梯度的积分算子，对所涉及的非局部性进行了新颖的重构。所提出的方法以统一的方式处理两种模型类型，并将先前的数学框架扩展到允许使用通用解相关系数函数的设置。将非本地运算符的先前形式与本文介绍的新形式进行比较，并通过具体示例突出了后者的优点。一维数值模拟提供了一些理论发现的例证。