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We study the propagation of singularities in solutions of linear convectionequations with spatially heterogeneous nonlocal interactions. A spatiallyvarying nonlocal horizon parameter is adopted in the model, which measures therange of nonlocal interactions. Via heterogeneous localization, this can leadto the seamless coupling of the local and nonlocal models. We are interested inunderstanding the impact on singularity propagation due to the heterogeneitiesof nonlocal horizon and the local and nonlocal transition. We firstanalytically derive equations to characterize the propagation of differenttypes of singularities for various forms of nonlocal horizon parameters in thenonlocal regime. We then use asymptotically compatible schemes to discretizethe equations and carry out numerical simulations to illustrate the propagationpatterns in different scenarios.

Numerical simulation of singularity propagation modeled by linear convection equations with spatially heterogeneous nonlocal interactions