R.M. Colombo, L. Giuzzi, F. Marcellini. Nash Equilibria in Traffic Networks with Multiple Populations and Origins–Destinations. Submitted, 2024.

R.M. Colombo, M. Garavello, F. Marcellini, E. Rossi. Hyperbolic Techniques in Epidemiological Modeling. Proceedings, proceedings of the XVIII International Conference on Hyperbolic Problems: Theory, Numerics, Applications, to appear, 2024.

M. Garavello, F. Marcellini. Autonomous Vehicles Driving Traffic: The Cauchy Problem. Communications in Mathematical Sciences, 22:  817–844, 2024.

R.M. Colombo, M. Garavello, F. Marcellini, E. Rossi.  General Renewal Equations Motivated by Biology and Epidemiology Journal of Differential Equations, 354: 133-169, 2023.

R.M. Colombo, F. Marcellini, E. Rossi. Vaccination Strategies through Intra-Compartmental Dynamics. Networks and Hetergeneous Media, 17:  385–400, 2022.

G. M. Coclite, N. De Nitti, M. Garavello, F. Marcellini. Vanishing viscosity for a 2×2 system modeling congested vehicular traffic, Networks and Hetergeneous Media, 16:  413–426, 2021.

F. Marcellini. The Follow-The-Leader Model without a Leader: an Infinite-Dimensional Cauchy Problem, Journal of Mathematical Analysis and Applications,  495: 124664, 21 pp. , 2021.

R.M. Colombo, M. Garavello, F. Marcellini, E. Rossi. An Age and Space Structured SIR Model Describing the Covid-19 Pandemic, Journal of Mathematics in Industry, 10, 22, 2020. 

R.M. Colombo, H. Holden, F. Marcellini. On the Microscopic Modeling of Vehicular Traffic on General Networks, SIAM Journal on Applied Mathematics, 80: 1377-1391, 2020.

M. Garavello, F. Marcellini. Global Weak Solutions to the Cauchy Problem for a Two-Phase Model at a Node, SIAM Journal on Mathematical Analysis, 52: 1567-1590, 2020.

T. Liard, F. Marcellini, B. Piccoli. The Riemann Problem for the GARZ Model with a Moving Constraint, AIMS on Applied Mathematics, Hyperbolic Problems: Theory, Numerics, Applications,  10: 524-530, 2020.

F. Marcellini. The Riemann Problem for a Two-Phase Model for Road Traffic with Fixed or Moving Constraints, Mathematical Biosciences and Engineering, 17: 1218-1232, 2020.

F. Marcellini. A Microscopic Model on a Traffic Network, Oberwolfach Report, 24: 46-49, 2019. 

M. Garavello, F. Marcellini, A Riemann Solver at a Junction compatible with a Homogenization Limit, Journal of Mathematical Analysis and Applications, 464: 1333-1351, 2018. 

M. Garavello, F. Marcellini, The Godunov Method for a 2-Phase Model, Communications in Applied and Industrial Mathematics, 9: 1-16, 2017. 

F. Marcellini, Existence of Solutions to a Boundary Value Problem for a Phase Transition Traffic Model, Networks and Hetergeneous Media, 12: 259-275, 2017.  

F. Marcellini, On the Stability of a Model for the Cutting of Metal Plates by Means of Laser Beams, Applied Mathematics Letters, 68: 143-149, 2017.  

M. Garavello, F. Marcellini, The Riemann Problem at a Junction for a Phase Transition Traffic Model, Discrete and Continuous Dynamical Systems-Series A-AIMS, 37: 5191-5209, 2017.  

F. Marcellini, A Traffic Model with Phase Transitions at a Junction, Oberwolfach Report, 12: 1720-1723, 2016.  

F. Marcellini, ODE-PDE Models in Traffic Flow Dynamics, Bulletin of the Brazilian Mathematical Society, New Series, 47: 533-544, 2016.   

R.M. Colombo, F. Marcellini, E. Rossi, Biological and Industrial Models Motivating Nonlocal Conservation Laws: a Review of Analytic and Numerical Results, Networks and Hetergeneous Media, 11: 49-67, 2016.   

R.M. Colombo, F. Marcellini, A Traffic Model Aware of Real Time Data, 2015, Mathematical Models and Methods in Applied Sciences, 26: 445-467, 2016.   

R.M. Colombo, F. Marcellini, NonLocal Systems of Balance Laws in Several Space Dimensions with Applications to Laser Technology, Journal of Differential Equations, 259: 6749-6773, 2015.  

R.M. Colombo, F. Marcellini, A Mixed ODE-PDE Model for Vehicular Traffic, Mathematical Methods in the Applied Sciences, 38: 1292-1302, 2015.  

 F. Marcellini, Free-Congested and Micro-Macro Descriptions of Traffic Flow, Discrete and Continuous Dynamical Systems-Series S-AIMS, 7: 543-556, 2014. 

F. Marcellini, Mixed Systems in the Description of Traffic Flow, Oberwolfach Report, 29: 37-40, 2013. 

 R. M. Colombo, G. Guerra, M. Herty, F. Marcellini, A Hyperbolic Model for the Laser Cutting Process, Applied Mathematical Modelling, 37: 7810-7821, 2013.  

R. M. Colombo, F. Marcellini, Smooth and Discontinuous Junctions in the p-System and in the 3x3 Euler System, Riv. Mat. Univ. Parma, 3: 55-69, 2012. 

G. Guerra, M. Herty, F. Marcellini, Modeling and Analysis of Pooled Stepped Chutes, Networks and Hetergeneous Media, 6: 665-679, 2011. 

F. Marcellini, Leggi di Conservazione nella Dinamica dei Gas e nei Flussi di Traffico. Matematica nella Società e nella Cultura, UMI, 3: 47-50, 2010.   

 R. M. Colombo, F. Marcellini, Coupling Conditions for the 3x3 Euler System, Networks and Hetergeneous Media, 5: 675-690, 2010. 

R. M. Colombo, F. Marcellini,  M. Rascle, A 2-Phase Traffic Model Based on a Speed Bound, SIAM Journal on Applied Mathematics, 70: 2652-2666, 2010.  

R. M. Colombo, F. Marcellini, Smooth and Discontinuous Junctions in the p-System, Journal of Mathematical Analysis and Applications, 361: 440-456, 2010.  

G. Guerra, F. Marcellini, V. Schleper, Balance laws with integrable unbounded sources, SIAM Journal on Mathematical Analysis, 41: 1164-1189, 2009.  

Outreach

R.M. Colombo, F. Marcellini. Traffico Veicolare e Dinamica di Pedoni Attraverso le Leggi di Conservazione. Quaderno 14, Dipartimento di Matematica e Fisica "Respighi", Piacenza, 2014.   PDF

PhD Thesis

F. Marcellini, Conservation Laws in Gas Dynamics and Traffic Flow. Università di Milano-Bicocca, PhD Thesis, 2009.  PDF