Publications

Books

  1. M. Garavello, B. Piccoli, Traffic Flow on Networks --- Conservation Laws Models, AIMS Series on Applied Mathematics, Vol. 1, American Institute of Mathematical Sciences, 2006. ISBN-13: 978-1-60133-000-0.

  2. M. Garavello, K. Han, B. Piccoli, Models for Vehicular Traffic on Networks, AIMS Series on Applied Mathematics, Vol. 9, American Institute of Mathematical Sciences, 2016. ISBN-13: 978-1-60133-019-2.

  3. A. Bayen, M.L. Delle Monache, M. Garavello, P. Goatin, B. Piccoli, Control problems for conservation laws with traffic applications. Modeling, analysis, and numerical methods, Progress in Nonlinear Differential Equations and Their Applications, Birkhäuser, 2022. ISBN: 978-3-030-93014-1.

Book Chapters

  1. M. Garavello, B. Piccoli, Optimal control, in Hanbook of Hybrid systems control, edited by J. Lunze and F. Lamnabhi-Lagarrigue, Cambridge University Press, 2009.

  2. M. Garavello, B. Piccoli, A multibuffer model for LWR road networks, in Advances in Dynamic Network Modeling in Complex Transportation Systems, Ukkusuri, Satish V.; Ozbay, Kaan (Eds.), Springer, 2013, X, 316 p. ISBN: 978-1-4614-6242-2.

  3. R. M. Colombo, M. Garavello, M. Lécureux-Mercier, Crowd Dynamics Through Conservation Laws, in Crowd Dynamics, Theory, Models, and Applications, Vol. 2, 2020, pp. 83-110.

Publications in International Journals

  1. C. D'Apice, M. Garavello, R. Manzo, B. Piccoli, Hybrid optimal control: case study of a car with gears, Internat. J. Control 76 (2003), pp. 1272-1284. (link to the paper)

  2. M. Garavello, Verifications theorems for Hamilton-Jacobi-Bellmann equations, SIAM J. Control Optim. 42 (no. 5) (2003), pp. 1623-1642. (link to the paper)

  3. M. Garavello, P. Soravia, Optimality principles and uniqueness for Bellman equation of unbounded control problems with discountinouos running cost, NoDEA. 11 (2004), pp. 271-298. (link to the paper)

  4. M. Garavello, B. Piccoli, Hybrid Necessary Principle, SIAM J. Control Optim. 43 (no. 5) (2005), pp. 1867-1887. (Abstract, link to the paper)

  5. G. M. Coclite, M. Garavello, B. Piccoli, Traffic Flow on a Road Network, SIAM J. Math. Anal. 36 (no. 6) (2005), pp. 1862-1886. (link to the paper)

  6. M. Garavello, B. Piccoli, Source-Destination Flow on a Roads Network, Commun. Math. Sci. 3 (no. 3) (2005), pp. 261-283. (link to the paper)

  7. M. Garavello, B. Piccoli, Traffic flow on a road network using the Aw-Rascle model, Comm. Partial Differential Equations 31 (no. 2) (2006), pp. 243-275. (link to the paper)

  8. M. Garavello, P. Soravia, Representation formulas for solutions of HJI equations with discontinuous coefficients and existence of value in differential games, J. Optim. Theory Appl. 130 (no. 2) (2006), pp. 209-229. (link to the paper, complete version)

  9. Y. Chitour, J.-M. Coron, M. Garavello, On conditions that prevent steady--state controllability of certain linear partial differential equations, Discrete Contin. Dyn. Syst. 14 (no. 4) (2006), pp. 643-672. (link to the paper)

  10. R. M. Colombo, M. Garavello, A Well Posed Riemann Problem for the p-System at a Junction, Netw. Heterog. Media 1 (no. 3) (2006), pp. 495-511. (link to the paper)

  11. M. Garavello, R. Natalini, B. Piccoli, A. Terracina, Conservation laws with discontinuous flux, Netw. Heterog. Media 2 (no. 1) (2007), pp. 159-179. (link to the paper)

  12. R. M. Colombo, M. Garavello, On the p-System at a Junction, Contemporary Mathematics 426, AMS, pp. 193-217.

  13. R. M. Colombo, M. Garavello, On the Cauchy Problem for the p-System at a Junction, SIAM J. Math. Anal. 39 (no. 5) (2008), pp. 1456-1471. (link to the paper)

  14. M. Garavello, E. Girejko, B. Piccoli, Generalized differentiation of parametrized families of trajectories, in Geometric control and nonsmooth analysis, 2008.

  15. M. Garavello, B. Piccoli, On fluido-dynamic models for urban traffic, Netw. Heterog. Media 4 (no. 1) (2009), pp. 107-126. (link to the paper)

  16. M. Garavello, B. Piccoli, Time-varying Riemann solvers for conservation laws on networks, J. Differential Equations 247 (2009), pp. 447-464, doi:10.1016/j.jde.2008.12.017. (link to the paper)

  17. M. Garavello, B. Piccoli, Conservation laws on complex networks, Ann. I. H. Poincaré AN 26 (2009), pp. 1925-1951, doi:10.1016/j.anihpc.2009.04.001. (link to the paper)

  18. G. M. Coclite, M. Garavello, Vanishing Viscosity for Traffic on Networks, SIAM J. Math. Anal. 42 (no. 4) (2010), pp. 1761-1783. (link to the paper)

  19. M. Garavello, B. Piccoli, Entropy type conditions for Riemann solvers at nodes, Adv. Differential Equations 16 (no. 1-2) (2011), pp. 113-144. (link to the journal)

  20. R. Borsche, R. M. Colombo, M. Garavello, On the Coupling of Systems of Hyperbolic Conservation Laws with Ordinary Differential Equations, Nonlinearity 23 (no. 11) (2010), pp. 2749--2770, doi: 10.1088/0951-7715/23/11/002. (link to the paper)

  21. M. Garavello, P. Goatin, The Aw-Rascle traffic model with locally constrained flow, J. Math. Anal. Appl. 378 (no. 2) (2011), pp. 634-648, doi:10.1016/j.jmaa.2011.01.033. (link to the paper)

  22. R. Borsche, R. M. Colombo, M. Garavello, Mixed Systems: ODEs-Balance Laws, J. Differential Equations 252 (no. 3) (2012), pp. 2311-2338, doi:10.1016/j.jde.2011.08.051. (link to the paper)

  23. R. M. Colombo, M. Garavello, M. Lécureux-Mercier, Non-local crowd dynamics, C. R. Acad. Sci. Paris, Ser. I 349 (2011), pp. 769-772, doi:10.1016/j.crma.2011.07.005. (link to the paper)

  24. M. Garavello, P. Goatin, The Cauchy problem at a node with buffer, Discrete Contin. Dyn. Syst. A, 32 (no. 6) (2012), pp. 1915-1938, doi: 10.3934/dcds.2012.32.1915. (link to the paper)

  25. R. M. Colombo, M. Garavello, M. Lécureux-Mercier, A Class of Non-Local Models for Pedestrian Traffic, Math. Models Methods Appl. Sci. 22 (no. 4) (2012), doi: 10.1142/S0218202511500230. (link to the paper)

  26. R. M. Colombo, F. Ferrari, M. Garavello, G. Maternini, 2–Phase Hyperbolic Models for Urban Traffic, International Journal of Roads and Airports 2 (no. 1) (2012), pp. 1-12, doi:10.5568/ijra.2012-02-01.112. (link to the paper)

  27. G. M. Coclite, M. Garavello, Vanishing viscosity for mixed systems with moving boundaries, J. Funct. Anal. 264 (no. 7) (2013), pp. 1664-1710, doi: 10.1016/j.jfa.2013.01.010.

  28. M. Garavello, B. Piccoli, Coupling of LWR and phase transition models at boundary, J. Hyperbolic Differ. Equ., 10 (no. 3) (2013), pp. 577-636, doi: 10.1142/S0219891613500215.

  29. M. Garavello, B. Piccoli, Coupling of microscopic and phase transition models at boundary, Netw. Heterog. Media 8 (no. 3) (2013), pp. 649-661, doi: 10.3934/nhm.2013.8.649.

  30. R. Borsche, R. M. Colombo, M. Garavello, On the Interactions between a Solid Body and a Compressible Inviscid Fluid, Interfaces Free Bound. 14 (2013), pp. 381--403, doi: 10.4171/IFB/307.

  31. M. Garavello, The LWR traffic model at a junction with multibuffers, Discrete Contin. Dyn. Syst. S 7 (no.3) (2014), pp. 463-482, doi:10.3934/dcdss.2014.7.463.

  32. A. Bressan, S. Canic, M. Garavello, M. Herty, B. Piccoli, Flows on networks: recent results and perspectives, EMS Surveys in Mathematical Sciences, EMS Surv. Math. Sci. 1 (2014), no. 1, pp. 47–111.

  33. R. M. Colombo, M. Garavello, Stability and Optimization in Structured Population Models on Graphs, Math. Biosci. Eng., 12 (no. 2) (2015), pp. 311-335, doi:10.3934/mbe.2015.12.311.

  34. R. Borsche, R. M. Colombo, M. Garavello, A. Meurer, Differential Equations Modeling Crowd Interactions, J Nonlinear Sci, 25 (no. 4) (2015), pp. 827-859, doi: 10.1007/s00332-015-9242-0.

  35. M. Garavello, Boundary Value Problem for a Phase Transition Model, Netw. Heterog. Media, 11 (2016), no. 1, pp. 89 - 105, doi: 10.3934/nhm.2016.11.89.

  36. R. M. Colombo, M. Garavello, Optimal Control in Renewable Resources Modeling, Bulletin of the Brazilian Mathematical Society, New Series, 47 (2016), no. 1, pp 347-357.

  37. R. M. Colombo, M. Garavello, Control of Biological Resources on Graphs, ESAIM: COCV, 23 (no. 3) (2017), pp. 1073-1097, doi: 10.1051/cocv/2016027.

  38. G. M. Coclite, M. Garavello, A Time Dependent Optimal Harvesting Problem with Measure Valued Solutions, SIAM J. Control Optim, 55 (no. 2) (2017), pp. 913-935, doi:10.1137/16M1061886.

  39. R. M. Colombo, M. Garavello, Polynomial Profits in Renewable Resources Management, Nonlinear Analysis Series B: Real World Applications 37 (2017), pp. 374–386, doi:10.1016/j.nonrwa.2017.03.002.

  40. M. Garavello, F. Marcellini, The Riemann problem at a junction for a phase transition traffic model, Discrete Contin. Dyn. Syst. A, 37 (no. 10) (2017), pp. 5191–5209. Doi: 10.3934/dcds.2017225.

  41. M. Garavello, F. Marcellini, The Godunov Method for a 2–Phase Model, Commun. Appl. Ind. Math. 8 (1), 2017, pp. 149–164, doi: 10.1515/caim-2017-0008.

  42. M. Garavello, S. Villa, The Cauchy problem for the Aw-Rascle-Zhang traffic model with locally constrained flow, J. Hyperbolic Differ. Equ., doi:10.1142/S0219891617500138.

  43. G. M. Coclite, M. Garavello, L. V. Spinolo, A mathematical model for piracy control and police response, Nonlinear Differ. Equ. Appl. (2017) 24: 48. Doi:10.1007/s00030-017-0471-9.

  44. M. Garavello, B. Piccoli, Boundary coupling of microscopic and first order macroscopic traffic models, NoDEA Nonlinear Differential Equations Appl. (2017) 24: 4. Doi:10.1007/s00030-017-0467-5.

  45. M. Garavello, F. Marcellini, A Riemann solver at a junction compatible with a homogenization limit, J. Math. Anal. Appl. 464 (no. 2) (2018), pp. 1333–1351. Doi: 10.1016/j.jmaa.2018.04.068.

  46. G. M. Coclite, M. Garavello, L.V. Spinolo, Optimal Strategies for a Time-Dependent Harvesting Problem, Discrete Contin. Dyn. Syst. S, 11 (no. 5) (2018), pp. 865-900. Doi: 10.3934/dcdss.2018053.

  47. F. Ancona, A. Cesaroni, G. M. Coclite, M. Garavello, On the optimization of conservation law models at a junction, SIAM J. Control Optim. 56 (no. 5) (2018), pp. 3370–3403. Doi: 10.1137/18M1176233.

  48. R. M. Colombo, M. Garavello, Hyperbolic consensus games, Commun. Math. Sci. 17 (2019), no. 4, pp. 1005–1024.

  49. R. M. Colombo, M. Garavello, Optimizing vaccination strategies in an age structured SIR model, Math. Biosci. Eng. 17 (2020), no. 2, pp. 1074–1089.

  50. M. Garavello, F. Marcellini, Global Weak Solutions to the Cauchy Problem for a Two-Phase Model at a Node, SIAM J. Math. Anal. 52 (2020), no. 2, pp. 1567-1590.

  51. M. Garavello, P. Goatin, T. Liard, B. Piccoli, A multiscale model for traffic regulation via autonomous vehicles, J. Differential Equations 269 (2020), no. 7, pp. 6088–6124.

  52. R. M. Colombo, M. Garavello, Well Posedness and Control in a NonLocal SIR Model, Applied Mathematics and Optimization 84 (2021), no. 1, pp. 737–771.

  53. R. M. Colombo, M. Garavello, On the 1D modeling of fluid flowing through a junction, Discrete Contin. Dyn. Syst. Ser. B 25 (2020), no. 10, pp. 3917-3929.

  54. R. M. Colombo, M. Garavello, F. Marcellini, E. Rossi, An age and space structured SIR model describing the Covid-19 pandemic, J. Math. Ind. 10 (2020), Paper No. 22, 20 pp.

  55. F. Ancona, A. Cesaroni, G. M. Coclite, M. Garavello, On optimization of traffic flow performance for conservation laws on networks, Minimax Theory Appl. 6 (2021), no. 2, pp. 205-226.

  56. R. M. Colombo, M. Garavello, Well Posedness and Control in Renewal Equations with NonLocal Boundary Conditions, Math. Methods Appl. Sci. 44 (2021), no. 14, pp. 11537–11564.

  57. G. M. Coclite, N. De Nitti, M. Garavello, F. Marcellini, Vanishing viscosity for a 2x2 system modeling congested vehicular traffic, Netw. Heterog. Media 16 (2021), no. 3, pp. 413–426.

  58. G. M. Coclite, M. Garavello, Measure optimal controls for models inspired by biology, SIAM J. Control Optim. 60 (no. 5) (2022), pp. 3051–3077. Doi: 10.1137/21M146332X.

Preprints

  1. R. Borsche, M. Eimer, M. Garavello, E. Rossi, Analysis of district heating networks, preprint 2021.

  2. R. M. Colombo, M. Garavello, Infectious Diseases Spreading Fought by Multiple Vaccines Having a Prescribed Time Effect, preprint 2021.

  3. R. Borsche, M. Garavello, D. Kocoglu, Switched Hyperbolic Balance Laws and Differential Algebraic Equations, preprint 2022.

  4. R. M. Colombo, M. Garavello, F. Marcellini, E. Rossi, General Renewal Equations Motivated by Biology and Epidemiology, preprint 2022.

  5. M. Garavello, F. Marcellini, Autonomous Vehicles Driving Traffic: The Cauchy Problem, preprint 2022.

Proceedings

  1. M. Garavello, B. Piccoli, Hybrid Necessary Principles: an application to a car with gears, Proceedings to IFAC Conference on Analysis and Design of Hybrid Systems, Saint-Malo, France, June 16-18, 2003.

  2. Y. Chitour, J.-M. Coron, M. Garavello, Obstructions for steady-state controllability, Control Systems: Theory, Numerics and Applications, Proocedings of Science, SISSA, 2005.

  3. M. Garavello, Verification Theorems for HJB equations, Control Systems: Theory, Numerics and Applications, Proocedings of Science, SISSA, 2005.

  4. M. Garavello, B. Piccoli, A Fluidodynamic Model for Traffic in a Road Network, proceeding of Traffic and Granular Flow '05, Springer, Berlin 2005.

  5. M. Garavello, B. Piccoli, Hybrid Necessary Principle, proceeding of 44th IEEE Conference on Decision and Control, Seville, 2005, doi: 10.1109/CDC.2005.1582242.

  6. Y. Chitour, J.-M. Coron, M. Garavello, On conditions that prevent steady-state controllability of certain linear partial differential equations, proceeding of 44th IEEE Conference on Decision and Control, Seville, 2005, doi: 10.1109/CDC.2005.1582299.

  7. R. M. Colombo, M. Garavello, Phase transition model for traffic at a junction, Transactions of the XXV International Seminar on Stability problems for Stochastic Models, Maiori, 2005.

  8. M. Garavello, R. Natalini, B. Piccoli, A. Terracina, A Riemann Solver Approach for Conservation Laws with Discontinuous Flux, in Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the Eleventh International Conference on Hyperbolic Problems, Lyon, July 17-21, 2006, pp. 1029-1036. S. Benzoni-Gavage, D. Serre Eds.

  9. R. M. Colombo, M. Garavello, Comparison Among Different Notions of Solution for the p-System at a Junction, proceeding of the The 7th AIMS Conference on Dynamical Systems and Differential Equations, Arlington, Texas, 2008.

  10. M. Garavello, B. Piccoli, Riemann solvers for conservation laws at a node, proceeding of the Hyperbolic problems: Theory, Numerics, and Applications, College Park, Maryland, U.S.A., 2008, in Proceedings of Symposia in Applied Mathematics, Volume 67, Part 2, pages 95-604, edited by E. Tadmor, J.-G. Liu, A. Tzavaras, AMS 2009.

  11. M. Garavello, Conservation laws at a node, proceedings of the IMA Summer Program on Conservation Laws, in Nonlinear Conservation Laws and Applications, The IMA Volumes in Mathematics and its Applications, Vol. 153. Bressan, A.; Chen, G.-Q.G.; Lewicka, M.; Wang, D. (Eds.). 2011.

  12. M. Garavello, A review of conservation laws on networks, proceedings of the New Trends in Model Coupling: Theory, Numerics and Applications, Parigi, Francia, 2009. In Netw. Heterog. Media 5 (no. 3) (2010), pp. 565-581. Special issue: New Trends in Model Coupling, Theory, Numerics and Applications.

  13. R. M. Colombo, M. Garavello, M. Lécureux-Mercier, N. Pogodaev, Conservation Laws in the Modeling of Moving Crowds, proceedings

    1. of the Fourteenth International Conference on Hyperbolic Problems. In “Hyperbolic Problems: Theory, Numerics, Applications”, AIMS on

    2. Applied Mathematics, Vol. 8, pp. 467–474, 2014.

  14. R. Borsche, R. M. Colombo, M. Garavello, Mixed systems with boundaries, proceedings of the Fourteenth International Conference on Hyperbolic Problems. In “Hyperbolic Problems: Theory, Numerics, Applications”, AIMS on Applied Mathematics, Vol. 8, pp. 575–582, 2014.