Two Dimensional Models of Multi-Lane Traffic Flow with Lane Changing Conditions

The first part of the talk is dedicated to the derivation on an advection-diffusion equation in two dimensions from a system of one dimensional hyperbolic PDEs modeling the macroscopic behavior of multi-lane traffic flow, taking lane changes into account. In the second part of the talk, we introduce the microscopic model the latter system originates from, and propose a generalisation of this model to two continuous space dimensions. We discuss its properties and well-posedness.