Papers, Proceedings, Lecture Notes & Book Chapters, Outreach.
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Rinaldo M. Colombo, Vincent Perrollaz, Abraham Sylla
Initial Data Identification in Space Dependent
Conservation Laws and Hamilton-Jacobi Equations
Communications in Partial Differential Equations, 49
(5-6), 470-504, 2024
Preprint, 2023
Rinaldo M. Colombo, Elena Rossi
Non Linear Hyperbolic-Parabolic Systems with Dirichlet
Boundary Conditions
Differential and Integral Equations, 37 (7/8), 443-478, 2024
Preprint, 2023
Rinaldo M. Colombo, Vincent Perrollaz, Abraham Sylla
Conservation Laws and Hamilton-Jacobi Equations with Space Inhomogeneity
Journal of
Evolution Equations, 23, 3, 50, 2023
Preprint, 2022
Rinaldo M. Colombo, Graziano Guerra, Yannick Holle
Well Posedness and Characterization of Solutions to Non
Conservative Products in Non Homogeneous Fluid Dynamics
Equations
Journal of Dynamics and Differential Equations, 2023
Preprint, 2022
Rinaldo M. Colombo, Mauro Garavello, Matthew Tandy
On the Coupling of Well Posed Differential Models
Nonlinear Analysis A: Theory, Methods &
Applications, Volume 232, 113290, 2023
Preprint, 2022
(detailed version)
Rinaldo M. Colombo, Mauro Garavello, Francesca Marcellini, Elena Rossi
General Renewal Equations Motivated by Biology and Epidemiology
Journal of Differential Equations, 354, 133-169, 2023
Preprint, 2022
Rinaldo M. Colombo, Mauro Garavello
Infectious Diseases Spreading Fought by Multiple Vaccines
Having a Prescribed Time Effect
Acta Biotheoretica, 71:1, 2023
Preprint, 2021
Rinaldo M. Colombo, Graziano Guerra, Yannick Holle
Non Conservative Products in Fluid Dynamics
Nonlinear Analysis: Real World Applications, 66, 103539, 2022
Preprint, 2021
Rinaldo M. Colombo, Elena Rossi
Well Posedness and Control in a Hyperbolic-Parabolic
Parasitoid-Parasite System
Studies in Applied Mathematics, 147, 3, 839-871, 2021
Preprint, 2020
Rinaldo M. Colombo, Mauro Garavello
Well Posedness and Control in a NonLocal SIR Model
Applied Mathematics and Optimization, 84, 1, 737-771,
2020
Preprint, 2019
Rinaldo M. Colombo, Mauro Garavello, Francesca Marcellini, Elena Rossi
An Age and Space Structured SIR Model Describing the Covid-19
Pandemic
Journal of Mathematics in Industry, 10, 1, 22, 2020
Preprint, 2020.
Rinaldo M. Colombo, Helge Holden, Francesca Marcellini
On the Microscopic Modeling of Vehicular Traffic on General Networks
SIAM Journal on Applied Mathematics, 80(3),
1377-1391, 2020
Preprint, 2019
Rinaldo M. Colombo, Vincent Perrollaz
Initial Data Identification in Conservation Laws and
Hamilton-Jacobi Equations
Journal de Mathématiques Pures et
Appliquées, 9, 138, 1-27, 2020
Preprint,
2019
Rinaldo M. Colombo, Mauro Garavello
Hyperbolic Consensus Games
Communications in Mathematical Sciences, 17, 4, 1005-1024, 2019
Preprint, 2018
Rinaldo M. Colombo, Elena Rossi
Modeling Crowd Movements in Domains with Boundaries
IMA Journal of Applied Mathematics 84, 5, 833-853, 2019
Rinaldo M. Colombo, Elena Rossi
Stability of the 1D IBVP for a Non Autonomous Scalar Conservation Law
Proceedings of the Royal Society of Edinburgh 149, 561-592, 2019
Preprint, 2016
Rinaldo M. Colombo, Elena Rossi
Nonlocal Conservation Laws in Bounded Domains
SIAM Journal on Mathematical Analysis, 50, 4,
4041-4065, 2018
Preprint,
2017
Rinaldo M. Colombo, Graziano Guerra
Conservation Laws with Coinciding Smooth Solutions but
Different Conserved Variables
Zeitschrift für Angewandte Mathematik und
Physik, 69, 2, 47, 2018
Preprint, 2017
Rinaldo M. Colombo, Elena Rossi
IBVPs for Scalar Conservation Laws with Time Discontinuous Fluxes
Mathematical Methods in the Applied Sciences, 41, 4, 1463-1479, 2018
Preprint, 2017
Rinaldo M. Colombo, Piotr Gwiazda, Magdalena Rosinska
Optimization in Structured Population Models through the
Escalator Boxcar Train
ESAIM - COCV, 24, 1, 377-399, 2018
Preprint, 2016
Rinaldo M. Colombo, Graziano Guerra
Uniqueness of the 1D Compressible to Incompressible Limit
Nonlinear Differential Equations and Applications, 24, 52, 2017
Preprint, 2016
Rinaldo M. Colombo, Mauro Garavello
Control of Biological Resources on Graphs
ESAIM - COCV, 23, 3, 1073-1097, 2017
Preprint, 2015
Rinaldo M. Colombo, Mauro Garavello
Polynomial Profits in Renewable Resources Management
Nonlinear Analysis: Real World Applications, 37, 374-386, 2017
Preprint, 2016
Rinaldo M. Colombo, Graziano Guerra
BV Solutions to 1D Isentropic Euler Equations in the Zero Mach Number Limit
Journal of Hyperbolic Differential Equations, 13, 4,
685-718, 2016
Preprint, 2015
Rinaldo M. Colombo, Helge Holden
Isentropic Fluid Dynamics in a Curved Pipe
Zeitschrift für Angewandte Mathematik und Physik, 67(5), 1-10, 2016
Preprint, 2015
Rinaldo M. Colombo, Francesca Marcellini
A Traffic Model Aware of Real Time Data
Mathematical Models and Methods in Applied Sciences, 26, 3, 445-467, 2016
Preprint, 2014
Rinaldo M. Colombo, Helge Holden
On the Braess Paradox with Nonlinear Dynamics and Control Theory
Journal of Optimization Theory and Applications, 168, 1, 216-230, 2016
Preprint, 2014
(arxiv)
Rinaldo M. Colombo, Graziano Guerra, Veronika Schleper
The Compressible to Incompressible Limit of 1D Euler Equations: the Non Smooth Case
Archive for Rational Mechanics and Analysis, 219, 2,
701-718, 2016
Preprint, 2013
Rinaldo M. Colombo, Francesca Marcellini
NonLocal Systems of Balance Laws in Several Space Dimensions with Applications to Laser Technology
Journal of Differential Equations, 259, 11, 6749-6773, 2015
Preprint, 2015
Raul Borsche, Rinaldo M. Colombo, Mauro Garavello, Anne Meurer
Differential Equations Modeling Crowd Interactions
Journal of Nonlinear Science, 25, 4, 827-859, 2015
Preprint, 2014
Rinaldo M. Colombo, Elena Rossi
Rigorous Estimates on Balance Laws in Bounded Domains
Acta Mathematica Scientia, 35, 4, 906-944, 2015
Preprint, 2015
Aekta Aggarwal, Rinaldo M. Colombo, Paola Goatin
Nonlocal Systems of Conservation Laws in Several Space
Dimensions
SIAM Journal on Numerical Analysis, 53, 2, 963-983, 2015
Preprint, 2014
Rinaldo M. Colombo, Francesca Marcellini
A Mixed ODE-PDE Model for Vehicular Traffic
Mathematical Methods in the Applied Sciences, 38, 7,
1292-1302, 2015
Preprint, 2013
Paulo Amorim,
Rinaldo M. Colombo, Andreia Teixeira
On the Numerical
Integration of Scalar Nonlocal Conservation Laws
ESAIM M2AN, 49, 1, 19-37, 2015
Preprint, 2013
Rinaldo M. Colombo, Mauro Garavello
Stability and Optimization in Structured Population Models on Graphs
Mathematical Biosciences and Engineering, 12, 2, 311-335, 2015
Preprint, 2014
Rinaldo M. Colombo, Elena Rossi
Hyperbolic Predators vs. Parabolic Prey
Communications in Mathematical Sciences, 13, 2, 369-400, 2015
Preprint, 2013
Rinaldo M. Colombo, Thomas Lorenz, Nikolay Pogodaev
On the Modeling of Moving Populations through Set Evolution Equations
Discrete and Continuous Dynamical Systems, Series A, 35, 1, 73-98, 2015
Preprint, 2013
Rinaldo M. Colombo, Nikolay Pogodaev
On the Control of Moving Sets: Positive and Negative Confinement Results
SIAM Journal on Control and Optimization, 51, 1, 380-401, 2013
Preprint
Rinaldo M. Colombo, Graziano Guerra, Wen Shen
Lipschitz Semigroup for an Integro-Differential Equation for Slow Erosion
Quarterly of Applied Mathematics, 70, 539-578, 2012
Preprint, 2011
Rinaldo M. Colombo, Nikolay Pogodaev
Confinement Strategies in a Model for the Interaction between Individuals and a Continuum
SIAM Journal on Applied Dynamical Systems, 11, 2, 741-770, 2012
Correlated videos.
Preprint
Rinaldo M. Colombo, Mauro Garavello, Magali Lécureux-Mercier
A Class of Non-Local Models for Pedestrian Traffic
Comptes Rendus Mathematique, 349, 769-772, 2011
Mathematical Models and Methods in Applied Sciences,
22, 4, 2012
Preprint, 2011
José A. Carrillo, Rinaldo M. Colombo, Piotr Gwiazda,
Agnieszka Ulikowska
Structured Populations, Cell Growth and Measure Valued Balance Laws
Journal of Differential Equations, 252, 4, 3245-3277, 2012
Preprint, 2011
Rinaldo M. Colombo, Magali Lécureux-Mercier
An Analytical Framework to Describe the Interactions Between Individuals and a Continuum
Journal of Nonlinear Science, 22, 1, 39-61, 2012
Preprint, 2010
Rinaldo M. Colombo, Graziano Guerra, Francesca Monti
Modeling the Dynamics of Granular Matter
IMA Journal of Applied Mathematics, 77, 2, 148-156, 2012
Preprint, 2009
Rinaldo M. Colombo, Magali Lécureux-Mercier
Nonlocal Crowd Dynamics Models for Several Populations
Acta Mathematica Scientia, 32, 1, 177-196, 2012
Preprint, 2011
Rinaldo M. Colombo, Michael Herty, Magali Mercier
Control of the Continuity Equation with a Non Local Flow
ESAIM COCV, 17, 2, 353-379, 2011
Preprint, 2009
Stefano Bianchini, Rinaldo M. Colombo, Francesca Monti
2×2 Systems of Conservation Laws with L∞ Data
Journal of Differential Equations 249, 12, 3466-3488, 2010
Preprint 2009
Raul Borsche, Rinaldo M. Colombo, Mauro Garavello
On the Coupling of Systems of Hyperbolic Conservation Laws with Ordinary Differential Equations
Nonlinearity 23, 11, 2749-2770, 2010
Preprint, 2010
Rinaldo M. Colombo, Francesca Marcellini, Michel Rascle
A 2-phase traffic model based on a speed bound
SIAM Journal on Applied Mathematics 70, 7, 2652-2666, 2010
Preprint, 2009
Rinaldo M. Colombo, Graziano Guerra
On General Balance Laws with Boundary
Journal of Differential Equations 248, 5, 1017-1043, 2010
Preprint, 2008
Rinaldo M. Colombo, Magali Mercier, Massimiliano D. Rosini
Stability and Total Variation Estimates on General Scalar Balance Laws
Communications in Mathematical Sciences 7, 1, 37-65, 2009
Comptes Rendus Mathematique, 347, 1-2, 45-48, 2009
Rinaldo M. Colombo, Graziano Guerra
Differential Equations in Metric Spaces with Applications
Discrete and Continuous Dynamical Systems, Series A 23, 3, 733-753, 2009
Preprint, 2007
Rinaldo M. Colombo, Graziano Guerra
Hyperbolic Balance Laws with a Dissipative Non Local Source
Communications on Pure and Applied Analysis 7, 5, 1077-1090, 2008
Preprint, 2007
Rinaldo M. Colombo, Graziano Guerra
Hyperbolic Balance Laws with a Non Local Source
Communications in Partial Differential Equations 32, 10-12, p.1917-1939, 2007
Preprint, 2007
Rinaldo
M. Colombo, Fabio S. Priuli
Characterization of Riemann Solvers for the Two Phase p-System
Communications in Partial Differential Equations, 28 (7&8), p.1371-1390, 2003
Preprint, 2002
Rinaldo M. Colombo, Mauro Garavello, Francesca Marcellini, Elena
Rossi
Hyperbolic Techniques in Epidemiological Modeling
Proceedings of the XVIII International Conference on
Hyperbolic Problems: Theory, Numerics, Applications, 2023
Rinaldo M. Colombo, Graziano Guerra, Yannick Holle
Balance Laws with Singular Source Term and Applications to
Fluid Dynamics
Proceedings of the XVIII International Conference on
Hyperbolic Problems: Theory, Numerics, Applications, 2023
Rinaldo M. Colombo
Well Posedness and Control in Models Based on Conservatuon
Laws
In Oberwolfach Reports, 11, 2021.
Rinaldo M. Colombo, Maria Gokieli, Massimiliano D. Rosini
Modeling Crowd Dynamics through Hyperbolic - Elliptic Equations
In Partial Differential Equations, Mathematical Physics,
and Stochastic Analysis A Volume in Honor of Helge Holden's
60th Birthday.
Editors: F. Gesztesy, H. Hanche-Olsen, E. Jakobsen, Y. Lyubarskii, N.H. Risebro e K. Seip.
Preprint 2016
Debora Amadori, Rinaldo M. Colombo, Graziano Guerra,
Wen Shen
Slow Erosion of Granular Flow: Continuous and Discontinuous
Profiles
In Hyperbolic Problems: Theory, Numerics, Applications,
641-650, HYP2012 conference editors: F.Ancona,
A.Bressan, P.Marcati, A.Marson, 2014.
Rinaldo M. Colombo, Paola Goatin, Massimiliano D. Rosini
On the Management of Vehicular and Pedestrian Flows
In Hyperbolic Problems: Theory, Numerics, Applications,
889-898, HYP2012 conference editors: F.Ancona,
A.Bressan, P.Marcati, A.Marson, 2014.
Raul Borsche, Rinaldo M. Colombo, Mauro Garavello
Mixed Systems with Boundaries
In Hyperbolic Problems: Theory, Numerics, Applications,
575-582, HYP2012 conference editors: F.Ancona,
A.Bressan, P.Marcati, A.Marson, 2014.
Rinaldo M. Colombo, Mauro Garavello, Magali Lécureux-Mercier,
Nikolay Pogodaev
Conservation Laws in the Modeling of Moving Crowds
In Hyperbolic Problems: Theory, Numerics, Applications,
467-475, HYP2012 conference editors: F.Ancona,
A.Bressan, P.Marcati, A.Marson, 2014.
Rinaldo M. Colombo, Michael Herty
Nodal Conditions for Hyperbolic Systems of Balance Laws
In Hyperbolic Problems: Theory, Numerics, Applications,
147-162, HYP2012 conference editors: F.Ancona,
A.Bressan, P.Marcati, A.Marson, 2014.
Rinaldo M. Colombo
Hyperbolic Conservation Laws and Ordinary Differential Equations
Thirteenth International Conference on ``Hyperbolic Problems: Theory, Numerics and Applications''
Series in Contemporary Applied Mathematics, CAM 17, Beijing, 2012
Rinaldo M. Colombo, Francesca Marcellini
Smooth and Discontinuous Junctions in the p-System and in the
3×3 Euler System
Proceedings of the Intensive Research Month on Hyperbolic
Conservation Laws and Fluid Dynamics, 01-28.02.2010,
Riv. Mat. Univ. Parma, 3, 1, 55-69, 2012.
Stefano Bianchini, Rinaldo M. Colombo, Francesca Monti
In Proceeding of the Seventh Meeting on Hyperbolic
Conservation Laws and Fluid Dynamics: Recent Results and
Research Perspectives, 2009, Riv. Mat. Univ. Parma, 1, 1,
p.189-204, 2010.
Rinaldo M. Colombo
Well Posedness and Control in Models Based on Conservation Laws
IMA Summer Program Nonlinear Conservation Laws and Applications, 2009
Preprint 2009
Rinaldo M. Colombo, Paola Goatin, Giulio Maternini, Massimiliano
D. Rosini
Macroscopic Models for Pedestrian Flows
Proceedings of the International Conference Big Events and
Transport
IUAV - TTL Research Unit, p.11-22, 2010
Rinaldo M. Colombo, Paola Goatin, Massimiliano D. Rosini
A Macroscopic Model for Pedestrian Flows in Panic Situations
Mathematical Sciences and Applications, 32, p.255-272, 2010
Rinaldo M. Colombo, Mauro Garavello
Comparison Among Different Notions of Solution for the p-System at a
Junction
Proceedings of The 7th AIMS Conference on Dynamical Systems and Differential Equations, Arlington, Texas, 2008
Discrete and Continuous Dynamical Systems, Supplement Volume, p.181-190, 2009
Rinaldo M. Colombo, Giancarlo Facchi, Giulio Maternini, Massimiliano D. Rosini
On the Continuum Modeling of Crowds
In Hyperbolic Problems: Theory, Numerics and Applications,
Hyp2008 conference
College Park, Maryland, USA. E. Tadmor, J.-G. Luo, A.E. Tzavaras editors
Proceedings of Symposia in Applied Mathematics, 67, 2, p.517-526, 2009
Rinaldo M. Colombo, Graziano Guerra
Balance Laws as Quasidifferential Equations in Metric
Spaces
In Hyperbolic Problems: Theory, Numerics and Applications,
Hyp2008 conference
College Park, Maryland, USA. E. Tadmor, J.-G. Luo, A.E. Tzavaras editors
Proceedings of Symposia in Applied Mathematics, 67, 2, p.527-536, 2009
Rinaldo M. Colombo, Paola Goatin, Giulio Maternini, Massimiliano D. Rosini
Using Conservation Laws in Pedestrian Modeling.
In Transport Management and Land-Use Effects in Presence of Unusual
Demand
Proceedings of the meeting SIDT 2009, L. Mussone, U. Crisalli editors. p.73-79, 2009
Rinaldo M. Colombo, Paola Goatin, Massimiliano D. Rosini
Conservation Laws with Unilateral Constraints in Traffic Modeling
In Applied and Industrial Mathematics in Italy III
E. De Bernardis, R. Spigler, V. Valente editors
Series on Advances in Mathematics for Applied Sciences, 82, p.244-255, 2009
Rinaldo M. Colombo, Mauro Garavello
On the p-System at a Junction
Contemporary Mathematics, 426, p.193-217, 2007
Rinaldo M. Colombo, Andrea Corli
On the Operator Splitting Method: Nonlinear Balance Laws and a Generalization of Trotter-Kato Formulas
Trends in Mathematics, VI, p.91-100, 2007
Rinaldo M. Colombo, Andrea Corli
On Source Terms in Multilane Traffic Models
Communications to SIMAI Congress, VIII SIMAI Congress, 2006
Rinaldo M. Colombo, Andrea Corli
Dynamic Parameters Identification in Traffic Flow Modeling
Discrete Continuous Dynamical Systems, suppl., p.190-199, 2005
Rinaldo M. Colombo, Giulio Maternini
A New Simulation Model for the Management of Unstable Traffic Flow
In New Technologies and Modeling for Roads: Applications to Design and Management
Atti del Convegno SIIV, Firenze 2004.
Rinaldo M. Colombo
Modeling and Managing Traffic Flow through Hyperbolic Conservation Laws
Proceedings of the conference Traffic and Granular Flow 2003
P.H.L. Bovy, S.P. Hoogendoorn, M. Schreckenberg, D.E. Wolf editors, p.229-234, 2005.
Patrizia Bagnerini, Rinaldo M. Colombo, Andrea Corli, Simone Pedretti
Conservation versus Balance Laws in Traffic Flow
Proceedings of the conference Traffic and Granular Flow 2003
P.H.L. Bovy, S.P. Hoogendoorn, M. Schreckenberg, D.E. Wolf editors, p.235-240, 2005.
Rinaldo M. Colombo, Alessandro Groli
Optimisation of a Conservation Law
Information Processing: Recent Mathematical Advances in Optimization and Control.
Mathematical and Computational Sciences Series
J. Cagnol, J.-P. Zolesio editors. Presses de l'Ecole des Mines de Paris, 2004.
Rinaldo M. Colombo, Andrea Corli
Phase Transitions and Chapman-Jouguet Combustions
In Hyperbolic problems: Theory, numerics, applications.
Proceedings of the Ninth International conference on Hyperbolic
problems CalTech, Pasadena, March 25-29, 2002, T.~Hou,
E.~Tadmor editors. Springer, p.463-472, 2003.
Rinaldo M. Colombo, Andrea Corli
Global Existence and Continuous Dependence of Phase
Transitions in Hyperbolic Conservation Laws
In Trends in Applications of Mathematics to Mechanics
G.Iooss, O.Guès, A.Nouri editors, CRC Monographs and
Surveys in Pure and Applied Mathematics 106, p.161-171, 2000.
Arrigo Cellina, Rinaldo M. Colombo
SomeQualitative and Quantitative Results on a Differential Inclusion
In Set-valued Analysis and Differential Inclusions,
A.B. Kurzhanski, V.M. Veliov editors, Birkhauser Boston, 16, 43-60,
1993.
Rinaldo M. Colombo, Magali Lecureux-Mercier, Mauro Garavello
Crowd Dynamics Through Conservation Laws
In Crowd Dynamics, Vol. 2, edited by L. Gibelli
Birkhäuser, 2020
Rinaldo M. Colombo
An Introductory Guide to References on Conservation Laws
Warsaw University, 2014
Rinaldo M. Colombo
Wave Front Tracking in Systems of Conservation Laws
Course delivered at the school Mathematical Theory in Fluid Mechanics
Applications of Mathematics, 49, 6, 501-537, 2004
Paseky, 2003
(Comments and criticisms on the notes below are warmly welcome!!!)
Rinaldo M. Colombo
Analisi Funzionale - Note Integrative
(In Italian. Revised 2011 edition)
Jim Utsler
A Focus on Science
IBM
Systems magazine, Power Systems - July 2020
Azmy S. Ackleh, Rinaldo M. Colombo, Paola Goatin, Adrian
Muntean, Sander Hille
Mathematical Modeling with Measures
Nieuw Archief voor Wiskunde, 20, 3, September 2019.