First-order aggregation models with alignment
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.
Cite
@article{arxiv.1505.07316,
title = {First-order aggregation models with alignment},
author = {Razvan C. Fetecau and Weiran Sun and Changhui Tan},
journal= {arXiv preprint arXiv:1505.07316},
year = {2016}
}