Sesión Análisis Numérico y Optimización

Structure Preserving multiscale methods for supercritical Fokker-Planck Equations

Tettamanti Horacio

Universita di Pavia, Italia   -   Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.

We focus on the construction of numerical schemes for Fokker–Planck equations with superlinear drifts that preserve key structural properties, such as non-negativity of the solution, entropy dissipation, and the correct large-time behavior. The proposed methods exploit the multiscale features of these equations and are capable of capturing condensation phenomena while converging to the steady state. These properties are essential for the correct description of the underlying physical problem which is linked to indistinguishable bosonic particles. Applications of the schemes to several nonlinear Fokker–Planck equations arising in Bose–Einstein condensation are presented.

Trabajo en conjunto con: Mattia Zanella (Universita di Pavia, Italia).

Referencias

[1] E. Calzola, G. Dimarco, G. Toscani, M. Zanella. Emergence of condensation patterns in kinetic equations for opinion dynamics, Physica D: Nonlinear Phenomena, Volume 470, Part A, 2024, 134356, ISSN 0167- 2789, https://doi.org/10.1016/j.physd.2024.134356.

[2] F. Franceschi, L. Pareschi, M. Zanella. (2025). Superlinear Drift in Consensus-Based Optimization with Condensation Phenomena. 10.48550/arXiv.2506.09001.

[3] G. Kaniadakis and P. Quarati. Classical model of bosons and fermions. Phys. Rev. E, 49:5103–5110, 1994.

[4] L. Pareschi and M. Zanella. Structure preserving schemes for nonlinear FokkerPlanck equations and applications. J. Sci. Comput., 74(3):1575–1600, 2018.

[5] G. Toscani, M. Zanella,(2024). Supercritical Fokker-Planck equations for consensus dynamics: large-time behaviour and weighted Nash-type inequalities. arXiv preprint arXiv:2411.01359.

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