nonlinear models

Deterministic particle approximation for nonlinear transport equations

Marco Di Francesco, Associate Professor, Department of Information Engineering, Computer Science and Mathematics, University of L'Aquila (Italy)

Feb 25, 14:00 - 15:00

Building L3 R3119

PDE numerical methods nonlinear models

Approximating the solution to an evolutionary partial differential equation by a set of "moving particles" has several advantages. It validates the use of a continuity equation in an "individuals-based" modeling setting, it provides a link between Lagrangian and Eulerian description, and it defines a "natural" numerical approach to those equations. I will describe recent rigorous results in that context. The main one deals with one-dimensional scalar conservation laws with nonnegative initial data, for which we prove that the a suitably designed "follow-the-leader" particle scheme approximates entropy solutions in the sense of Kruzkov in the many particle limit. Said result represents a new way to solve scalar conservation laws with bounded and integrable initial data. The same method applies to second order traffic flow models, to nonlocal transport equations, and to the Hughes model for pedestrian movements.