Supercritical Mass and Condensation in Fokker--Planck Equations for Consensus Formation
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911671439589376 |
|---|---|
| author | Caloi, Monica Zanella, Mattia |
| author_facet | Caloi, Monica Zanella, Mattia |
| contents | Inspired by recently developed Fokker--Planck models for Bose--Einstein statistics, we study a consensus formation model with condensation effects driven by a polynomial diffusion coefficient vanishing at the domain boundaries. For the underlying kinetic model, given by a nonlinear Fokker--Planck equation with superlinear drift, it was shown that if the initial mass exceeds a critical threshold, the solution may exhibit finite-time concentration in certain parameter regimes. Here, we show that this supercritical mass phenomenon persists for a broader class of diffusion functions and provide estimates of the critical mass required to induce finite-time loss of regularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13276 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Supercritical Mass and Condensation in Fokker--Planck Equations for Consensus Formation Caloi, Monica Zanella, Mattia Analysis of PDEs Multiagent Systems Adaptation and Self-Organizing Systems Inspired by recently developed Fokker--Planck models for Bose--Einstein statistics, we study a consensus formation model with condensation effects driven by a polynomial diffusion coefficient vanishing at the domain boundaries. For the underlying kinetic model, given by a nonlinear Fokker--Planck equation with superlinear drift, it was shown that if the initial mass exceeds a critical threshold, the solution may exhibit finite-time concentration in certain parameter regimes. Here, we show that this supercritical mass phenomenon persists for a broader class of diffusion functions and provide estimates of the critical mass required to induce finite-time loss of regularity. |
| title | Supercritical Mass and Condensation in Fokker--Planck Equations for Consensus Formation |
| topic | Analysis of PDEs Multiagent Systems Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2602.13276 |