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Speaker: Mattia Zanella, Professor, Dept of Mathematics, Universita di Pavia
Title: Superlinear Drifts trigger finite-time blow-up in kinetic consensus dynamics
Abstract: In this talk, we introduce a new class of kinetic equations designed to explore the impact of initial mass on consensus formation dynamics. Specifically, we investigate the effects of superlinear drifts in kinetic Kaniadakis-Quarati-type equations, originally developed to model the dynamics of quantum indistinguishable particles in a spatially homogeneous setting. From the resulting PDE governing the evolution of the particle density, we identify the regimes where a critical mass triggers finite-time blow-up of the solution. Additionally, we discuss the regularity properties of the solutions for these models.