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math.AP2026

The nonlocal attraction-repulsion transport equation with power kernels

Massimo Fornasier, Hui Huang, Lukang Sun

We study a nonlocal continuity equation on in which a probability density is driven by the competition between attraction toward a prescribed background measure …

math.AP2026

Well-posedness and Smoothing Effect of the Porous Media Equation under Poincaré Inequality

Lukang Sun

We study the Cauchy problem for a weighted porous medium equation on associated with a Gibbs probability measure . Under a Poincaré inequality for and the con…

math.AP2026

Large-Time Analysis of the Langevin Dynamics for Energies Fulfilling Polyak-Łojasiewicz Conditions

Massimo Fornasier, Lukang Sun, Rachel Ward

In this work, we take a step towards understanding overdamped Langevin dynamics for the minimization of a general class of objective functions . We establish well-pose…

math.AP2025

Regularity and positivity of solutions of the Consensus-Based Optimization equation: unconditional global convergence

Massimo Fornasier, Lukang Sun

Introduced in 2017 \cite{B1-pinnau2017consensus}, Consensus-Based Optimization (CBO) has rapidly emerged as a significant breakthrough in global optimization. This straightforward…