06/05/2026, 17:00 — 18:00 Europe/Lisbon —
Online
Théophile Dolmaire, Università degli Studi dell'Aquila, Italy
An Alexander’s theorem for inelastic hard spheres
When studying systems of particles, the very first step before any qualitative analysis is to establish the well-posedness of the dynamics of the system. In the case of hard spheres, whose trajectories are piecewise affine, the singularities arising at collision events prevent the direct use of Cauchy-Lipschitz-type of arguments. This issue was addressed by Alexander (1975) in the elastic case, where the kinetic energy is conserved during the collisions. For dissipative systems, the question remains largely open, due to the possibility that infinitely many collisions take place in finite time, a phenomenon known as inelastic collapse. We will discuss the case of a particular class of inelastic hard sphere systems, in which a fixed amount of kinetic energy is lost in each sufficiently energetic collision. The results were obtained in collaboration with Juan J. L. Velázquez (Universität Bonn), and are published in arXiv:2403.02162v2 (to appear in Communications in Mathematical Physics).
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