English

Mean field limit for one dimensional opinion dynamics with Coulomb interaction and time dependent weights

Analysis of PDEs 2023-12-07 v2

Abstract

The mean field limit with time dependent weights for a 1D singular case, given by the attractive Coulomb interactions, is considered. This extends recent results [1,8] for the case of regular interactions. The approach taken here is based on transferring the kinetic target equation to a Burgers-type equation through the distribution function of the measures. The analysis leading to the stability estimates of the latter equation makes use of Kruzkov entropy type estimates adapted to deal with nonlocal source terms.

Keywords

Cite

@article{arxiv.2306.01099,
  title  = {Mean field limit for one dimensional opinion dynamics with Coulomb interaction and time dependent weights},
  author = {Immanuel Ben Porat and José A. Carrillo and Sondre T. Galtung},
  journal= {arXiv preprint arXiv:2306.01099},
  year   = {2023}
}

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27 pages