We study the propagation of singularities in solutions of linear convection equations with spatially heterogeneous nonlocal interactions. A spatially varying nonlocal horizon parameter is adopted in the model, which measures the range of nonlocal interactions. Via heterogeneous localization, this can lead to the seamless coupling of the local and nonlocal models. We are interested in understanding the impact on singularity propagation due to the heterogeneities of nonlocal horizon and the local and nonlocal transition. We first analytically derive equations to characterize the propagation of different types of singularities for various forms of nonlocal horizon parameters in the nonlocal regime. We then use asymptotically compatible schemes to discretize the equations and carry out numerical simulations to illustrate the propagation patterns in different scenarios.
翻译:我们研究单点在线性对流方程式解决方案中的传播与空间差异性非局部互动的解决方案。模型采用了一个空间差异化的非本地地平线参数,该参数测量非本地互动的范围。通过异点化,这可能导致本地模型和非本地模型的无缝结合。我们有兴趣了解非本地地平线差异性和地方和非本地转型对单点传播的影响。我们首先通过分析推算方程式,确定非本地系统中不同形式非本地地平线参数不同类型单点的传播特征。我们随后使用非现点兼容的方程式将方程式分离,并进行数字模拟,以说明不同情景中的传播模式。