First-order aggregation models with alignment

@article{Fetecau2016FirstorderAM,
  title={First-order aggregation models with alignment},
  author={Razvan C. Fetecau and Weiran Sun and Changhui Tan},
  journal={Physica D: Nonlinear Phenomena},
  year={2016},
  volume={325},
  pages={146-163}
}
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 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… Expand

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