Rinaldo M. Colombo (home, MathSci profile, Zentralblatt profile, researchID, Google scholar)

Selected Publications

Papers	Proceedings	Lecture Notes
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Papers

Preprints To appear 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 Before

Preprints

Rinaldo M. Colombo, Nikolay Pogodaev
Confinement Strategies in a Model for the Interaction between Individuals and a Continuum
Preprint, 2011

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To appear

Rinaldo M. Colombo, Veronika Schleper
Two-Phase Flows: Non-smooth Well Posedness and the Compressible to Incompressible Limit
To appear on Nonlinear Analysis: Real World Applications

Rinaldo M. Colombo, Graziano Guerra, Wen Shen
Lipschitz Semigroup for an Integro-Differential Equation for Slow Erosion
To appear on Quarterly of Applied Mathematics.

José A. Carrillo, Rinaldo M. Colombo, Piotr Gwiazda, Agnieszka Ulikowska
Structured Populations, Cell Growth and Measure Valued Balance Laws
To appear on Journal of Differential Equations.

Rinaldo M. Colombo, Mauro Garavello, Magali Lécureux-Mercier
A Class of Non-Local Models for Pedestrian Traffic
Comptes Rendus Mathematique, 349, 769-772, 2011
To appear on Mathematical Models and Methods in the Applied Sciences.
Preprint, 2011

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2012

Rinaldo M. Colombo, Magali Lécureux-Mercier
An Analytical Framework to Describe the Interactions Between Individuals and a Continuum
Journal of Nonlinear Science, 22, 39-61, 2012

Raul Borsche, Rinaldo M. Colombo, Mauro Garavello
Mixed Systems: ODEs - Balance Laws
Journal of Differential Equations, 252, 2311-2338, 2012

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2011

Rinaldo M. Colombo, Magali Lécureux-Mercier
Nonlocal Crowd Dynamics Models for Several Populations
Acta Mathematica Scientia, 32, 1, 177-196, 2011.

Anna Cattani, Rinaldo M. Colombo, Graziano Guerra
A Hyperbolic Model for Granular Flow
Zeitschrift für Angewandte Mathematik und Mechanik, 92, 1, 72-88, 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

Rinaldo M. Colombo, Graziano Guerra, Francesca Monti
Modeling the Dynamics of Granular Matter
IMA Journal of Applied Mathematics, 1-17, 2011 (Preprint)

Rinaldo M. Colombo, Paola Goatin, Massimiliano D. Rosini
On the Modeling and Management of Traffic
ESAIM M2AN 45, 853-872, 2011

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2010

Rinaldo M. Colombo, Francesca Marcellini
Coupling Conditions for the 3×3 Euler System
Networks and Hetergeneous Media 5, 4, 675-690, 2010

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

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)

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

Rinaldo M. Colombo, Paola Goatin, Benedetto Piccoli
Road Networks with Phase Transitions
Journal of Hyperbolic Differential Equations 7, 1, 85-106, 2010

Rinaldo M. Colombo, Graziano Guerra
On General Balance Laws with Boundary
Journal of Differential Equations 248, 5, 1017-1043, 2010

Rinaldo M. Colombo, Francesca Marcellini
Smooth and Discontinuous Junctions in the p-System
Journal of Matematical Analysis and Applications 361, 2, 440-456, 2010

Rinaldo M. Colombo, Francesca Monti
Solutions with Large Total Variation to Nonconservative Hyperbolic Systems
Communications on Pure and Applied Analysis 9, 1, 47-60, 2010

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2009

Rinaldo M. Colombo, Graziano Guerra, Michael Herty, Veronika Sachers
Modeling and Optimal Control of Networks of Pipes and Canals
SIAM Journal on Control and Optimization 48, 3, 2032-2050, 2009

Rinaldo M. Colombo, Massimiliano D. Rosini
Existence of Nonclassical Solutions in a Pedestrian Flow Model
Nonlinear Analysis: Real World Applications 10, 5, 2716-2728, 2009

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

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2008

Rinaldo M. Colombo, Michael Herty, Veronika Sachers
On 2×2 Conservation Laws at a Junction
SIAM Journal on Mathematical Analysis 40, 2, 605-622, 2008

Rinaldo M. Colombo, Cristina Mauri
Euler System for Compressible Fluids at a Junction
Journal of Hyperbolic Differential Equations 5, 3, 547-568, 2008

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

Daniela Calvo, Rinaldo M. Colombo, Hermano Frid
L¹ Stability of Spatially Periodic Solutions in Relativistic Gas Dynamics
Communications in Mathematical Physics 284, 2, p.509-535, 2008

Rinaldo M. Colombo, Graziano Guerra
On the Stability Functional for Conservation Laws
Nonlinear Analysis: Theory, Methods & Applications 69, 5-6, p.1581-1598, 2008

Rinaldo M. Colombo, Mauro Garavello
On the Cauchy Problem for the p-System at a Junction
SIAM Journal on Mathematical Analysis 39, 5, p.1456-1471, 2008

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2007

Rinaldo M. Colombo, Massimiliano D. Rosini
Well Posedness of Balance Laws with Non-Characteristic Boundary
Bollettino dell'Unione Matematica Italiana (8), 10-B, p.875-894, 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

Rinaldo M. Colombo, Andrea Corli, Massimiliano D. Rosini
Non Local Balance Laws in Traffic Models and Crystal Growth
Zeitschrift für Angewandte Mathematik und Mechanik, 87, 6, p.449-461, 2007

Rinaldo M. Colombo, Paola Goatin
A Well Posed Conservation Law with a Variable Unilateral Constraint
Journal of Differential Equations, 234, 2, p.654-675, 2007

Rinaldo M. Colombo, Paola Goatin, Fabio S. Priuli
Global Well Posedness of a Traffic Flow Model with Phase Transitions
Nonlinear Analysis: Theory, Methods & Applications, 66, No. 11 (A), p.2413-2426, 2007

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2006

Rinaldo M. Colombo, Andrea Corli
Well Posedness for Multilane Traffic Models
Annali dell'Università di Ferrara Sez. VII Sci. Mat. 52, 2, 291-301, 2006

Rinaldo M. Colombo, Mauro Garavello
A Well Posed Riemann Problem for the p-System at a Junction
Networks and Heterogeneous Media, 1, 3, p.495-511, 2006

Patrizia Bagnerini, Rinaldo M. Colombo, Andrea Corli
On the Role of Source Terms in Continuum Traffic Flow Models
Mathematical and Computer Modelling, 44, 9-10, p.917-930, 2006

Sylvie Benzoni-Gavage, Rinaldo M. Colombo, Piotr Gwiazda
Measured Valued Solutions to Conservation Laws Motivated by Traffic Modeling
Proceedings of the Royal Society A, 462, 2070, p.1791-1803, 2006

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2005

Rinaldo M. Colombo, Piotr Gwiazda
Sensitivity from the Constitutive Relations in Materials with Memory
Continuum Mechanics and Thermodynamics, 17, 2, p.159-164, 2005

Rinaldo M. Colombo, Piotr Gwiazda
L¹ Stability of Semigroups with respect to their Generators
Quarterly of Applied Mathematics, 63, 3, p.509-526, 2005

Rinaldo M. Colombo, Massimiliano D. Rosini
Pedestrian Flows and Nonclassical Shocks
Mathematical Methods in the Applied Sciences, 28, 13, p.1553-1567, 2005

Rinaldo M. Colombo, Massimiliano D. Rosini
Well Posedness of Balance Laws with Boundary
Journal of Mathematical Analysis and Applications, 311, 2, p.683-702, 2005

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2004

Rinaldo M. Colombo, Andrea Corli
Sonic and Kinetic Phase Transitions with Applications to Chapman-Jouguet Deflagrations
Mathematical Methods in the Applied Sciences, 27, p.843-864, 2004

Rinaldo M. Colombo, Andrea Corli
Stability of the Riemann Semigroup with Respect to the Kinetic Condition
Quarterly of Applied Mathematics, 62, 3, p.541-551, 2004

Rinaldo M. Colombo, Andrea Corli
A Semilinear Structure on Semigroups in a Metric Space
Semigroup Forum, 68, 3, p.419-444, 2004

Rinaldo M. Colombo, Andrea Corli
On a Class of Hyperbolic Balance Laws
Journal of Hyperbolic Differential Equations, 1, 4, p.725-745, 2004

Rinaldo M. Colombo, Alessandro Groli
On the Optimization of a Conservation Law
Calculus of Variations and P.D.E.s, 19, 3, p.269-280, 2004

Rinaldo M. Colombo, Alessandro Groli
Minimising Stop and Go Waves to Optimise Traffic Flow
Applied Mathematics Letters, 17, 6, p.697-701, 2004

Rinaldo M. Colombo, Alessandro Groli
On the Initial Boundary Value Problem for Temple Systems
Nonlinear Analysis: Theory, Methods & Applications, 56/4, p.569-589, 2004

Rinaldo M. Colombo, Alessandro Groli
On the Optimization of the Initial Boundary Value Problem for a Conservation Law
Journal of Mathematical Analysis and Applications, 291/1, p.82-99, 2004

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2003

Sylvie Benzoni - Gavage, Rinaldo M. Colombo
An n-Populations Model for Traffic Flow
European Journal of Applied Mathematics, 14, n°5, p.587-612, 2003

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

Rinaldo M. Colombo, Andrea Marson
A Hölder Continuous ODE Related to Traffic Flow
Proceedings of the Royal Society of Edinburgh, Section A 133, 4, p.759-772, 2003

Rinaldo M. Colombo, Andrea Corli
On 2×2 Conservation Laws with Large Data
Nonlinear Differential Equations and Applications 10, 3, p.255-268, 2003

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2002

Stefano Bianchini, Rinaldo M. Colombo
On the Stability of the Standard Riemann Semigroup
Proceedings of the American Mathematical Society, 130, n°7, p.1961-1973, 2002

Rinaldo M. Colombo
On a 2×2 Hyperbolic Traffic Flow Model
Mathematical and Computer Modeling, p.35-36, 2002

Rinaldo M. Colombo
Hyperbolic Phase Transitions in Traffic Flow
SIAM Journal on Applied Mathematics, 63 (2), p.708-721, 2002

Rinaldo M. Colombo, Andrea Corli
Sonic Hyperbolic Phase Transitions and Chapman Jouguet Detonations
Journal of Differential Equations, 184, p.321-347, 2002

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Before

Rinaldo M. Colombo, Andrea Corli
Continuous Dependence in Conservation Laws with Phase Transitions
SIAM Journal of Mathematical Analysis, 31 (1), p.34-62, 1999

Alberto Bressan, Rinaldo M. Colombo
Decay of Positive Waves in Nonlinear Systems of Conservation Laws
Annali della Scuola Normale Superiore, Pisa Cl. Sci. (4), 26 (1), p.133-160, 1998

Rinaldo M. Colombo, Nils H. Risebro
Continuous Dependence in the Large for Some Equations of Gas Dynamics
Communications in Partial Differential Equations, 23 (9 &10), p.1693-1718, 1998

Debora Amadori, Rinaldo M. Colombo
Continuous Dependence for 2×2 Conservation Laws with Boundary
Journal of Differential Equations, 138 (2), p.229-266, 1997

Alberto Bressan, Rinaldo M. Colombo
The Semigroup Generated by 2×2 Conservation Laws
Archive for Rational Mechanics and Analysis, 133 (1), p.1-75, 1995

Alberto Bressan, Rinaldo M. Colombo
Unique Solutions of 2×2 Conservation Laws with Large Data
Indiana University Mathematics Journal, 44 (3), p.677-725, 1995

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Proceedings

As Contributor

Rinaldo M. Colombo
Well Posedness and Control in Models Based on Conservation Laws
IMA Summer Program Nonlinear Conservation Laws and Applications, 2009

Rinaldo M. Colombo
Phase Transitions in Car Traffic & Pedestrian Flow Modeling
Oberwolfach Report 0809b, p.520-523, 2008

Rinaldo M. Colombo, Graziano Guerra
Non Local Sources in Hyperbolic Conservation Laws with Applications
Eleventh International Conference on Hyperbolic Problems Theory, Numerics, Applications, 2008

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, Mauro Garavello
On the p-System at a Junction
Contemporary Mathematics, 426, p.193-217, 2007

Rinaldo M. Colombo, Andrea Corli
On Source Terms in Multilane Traffic Models
Communications to SIMAI Congress, VIII SIMAI Congress, 2006

Rinaldo M. Colombo, Paola Goatin
Traffic Flow Models with Phase Transitions
Flow, Turbulence and Combustion, 76, 4, p.383-390, 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
Phase Transitions in Hyperbolic Conservation Laws
Progress in analysis, Vol. I, II (Berlin, 2001), p.1279-1287, World Scientific, 2003

Rinaldo M. Colombo
Phase Transitions in a Traffic Flow Model
Proceedings in Applied Mathematics and Mechanics 3, p.20-23, 2003

Rinaldo M. Colombo, Andrea Marson
Conservation laws and O.D.E.s. A traffic problem
Hyperbolic problems: theory, numerics, applications, p.455-461, Springer, Berlin, 2003