Mean-field limit for collective behavior models with sharp sensitivity regions

Abstract

We rigorously show the mean-field limit for a large class of swarming\nindividual based models with local sharp sensitivity regions. For instance,\nthese models include nonlocal repulsive-attractive forces locally averaged over\nsharp vision cones and Cucker-Smale interactions with discontinuous\ncommunication weights. We construct global-in-time defined notion of solutions\nthrough a differential inclusion system corresponding to the particle\ndescriptions. We estimate the error between the solutions to the differential\ninclusion system and weak solutions to the expected limiting kinetic equation\nby employing tools from optimal transport theory. Quantitative bounds on the\nexpansion of the 1-Wasserstein distance along flows based on a weak-strong\nstability estimate are obtained. We also provide different examples of\nrealistic sensitivity sets satisfying the assumptions of our main results.\n