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arXiv · 1505.07316

First-order aggregation models with alignment

Razvan C. Fetecau·Weiran Sun·Changhui Tan
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Abstract

We include alignment interactions in a well-studied first-order attractive-repulsive macroscopic model for aggregation. The distinctive feature of the extended model is that the equation that specifies the velocity in terms of the population density, becomes {\em implicit}, and can have non-unique solutions. We investigate the well-posedness of the model and show rigorously how it can be obtained as a macroscopic limit of a second-order kinetic equation. We work within the space of probability measures with compact support and use mass transportation ideas and the characteristic method as essential tools in the analysis. A discretization procedure that parallels the analysis is formulated and implemented numerically in one and two dimensions.

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Razvan C. Fetecau, Weiran Sun, Changhui Tan. 2015-05-27. First-order aggregation models with alignment. https://doi.org/10.1016/j.physd.2016.03.011

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