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<p>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.</p>

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Supercritical mass and condensation in Fokker-Planck equations for consensus formation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月22日

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  • Monica Caloi,
  • Mattia Zanella

摘要

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.