16:00-17:00 Monday, 7 April 2025 Auditorium, Rectorate
Abstract
Consider a so-called nonlocal conservation law, which is a continuity equation where the velocity field depends on the solution through the convolution with a given kernel. In the singular limit where the convolution kernel is replaced by a Dirac delta, one formally recovers a scalar conservation law. In this talk I will address the following question: can we rigorously justify this formal limit? In general, this is not possible, as shown by explicit counter-examples. However, in the specific framework of traffic models (with anisotropic convolution kernels) various authors have recently established convergence results, under suitable assumptions. My presentation will be based on joint works with Maria Colombo, Gianluca Crippa, and Elio Marconi.