11 citations · 13 across the 10 of their papers we have counts for
14 papers · 1 filter
Well-posedness and numerical approximation of nonlinear conservation laws with hysteresis
Paola Goatin, Stefan Moreti
This article studies the Cauchy problem for the scalar conservation law \[ \partial_t u + \partial_t w + \partial_x f(u) = 0, \] where is the outpu…
Non-local traffic flow models with time delay: well-posedness and numerical approximation
Ilaria Ciaramaglia, Paola Goatin, Gabriella Puppo
We prove the well-posedness of weak entropy solutions of a scalar non-local traffic flow model with time delay. Existence is obtained by convergence of finite volume approximate so…
The mathematical theory of Hughes' model: a survey of results
Debora Amadori, Boris Andreianov, Marco Di Francesco +9
We provide an overview of the results on Hughes' model for pedestrian movements available in the literature. After the first successful approaches to solving a regularised version…
A multiscale model for traffic regulation via autonomous vehicles
Mauro Garavello, Paola Goatin, Thibault Liard +1
Autonomous vehicles (AVs) allow new ways of regulating the traffic flow on road networks. Most of available results in this direction are based on microscopic approaches, where ODE…
A multi-lane macroscopic traffic flow model for simple networks
Paola Goatin, Elena Rossi
We prove the well-posedness of a system of balance laws inspired by [8], describing macro-scopically the traffic flow on a multi-lane road network. Motivated by real applications,…
Well-posedness of a non-local model for material flow on conveyor belts
Elena Rossi, Jennifer Kötz, Paola Goatin +1
In this paper, we focus on finite volume approximation schemes to solve a non-local material flow model in two space dimensions. Based on the numerical discretisation with dimensio…