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- Title
Local Well-Posedness and Sensitivity Analysis for the Self-Organized Kinetic Model.
- Authors
Jiang, Ning; Zhang, Zeng
- Abstract
We consider the self-organized kinetic model (SOK), which was derived as the mean field limit of the Couzin-Vicsek algorithm. This model yields a singularity when the particle flux vanishes. By showing that the singularity does not happen in finite time, we obtain local existence and uniqueness of smooth solutions to SOK. Furthermore, considering uncertainties in the initial data and in the interaction kernel, we analyze the random SOK model (RSOK). We provide local sensitivity analysis to justify the regularity with respect to the random parameter and the stability of solutions to RSOK.
- Publication
Acta Applicandae Mathematicae, 2021, Vol 176, Issue 1, p1
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-021-00457-8