Edit Profile (opens in new tab) Colombo, Rinaldo M. Co-Author Distance Author ID: colombo.rinaldo-m Published as: Colombo, Rinaldo M.; Colombo, R. M. Homepage: http://rinaldo.unibs.it External Links: MGP · ORCID · Wikidata · Google Scholar · dblp · GND · IdRef · theses.fr Documents Indexed: 156 Publications since 1990, including 8 Additional arXiv Preprints 11 Contributions as Editor · 1 Further Contribution Co-Authors: 71 Co-Authors with 158 Joint Publications 1,970 Co-Co-Authors all top 5 Co-Authors 10 single-authored 28 Garavello, Mauro 20 Guerra, Graziano 17 Rossi, Elena 15 Corli, Andrea 13 Marcellini, Francesca 12 Rosini, Massimiliano Daniele 10 Goatin, Paola 6 Bianchini, Stefano 6 Lécureux-Mercier, Magali 6 Marson, Andrea 4 Borsche, Raul 4 Bressan, Alberto 4 Groli, Alessandro 4 Gwiazda, Piotr 4 Herty, Michael Matthias 4 LeFloch, Philippe Gerard 4 Monti, Francesca 4 Perrollaz, Vincent 4 Pogodaev, Nikolaĭ Il’ich 3 Ancona, Fabio 3 Cellina, Arrigo 3 Holden, Helge 3 Mercier, Magali 3 Piccoli, Benedetto 3 Rohde, Christian 3 Schleper, Veronika 3 Sylla, Abraham 2 Amadori, Debora 2 Bagnerini, Patrizia 2 Benzoni-Gavage, Sylvie 2 Holle, Yannick 2 Karlsen, Kenneth Hvistendahl 2 Lagoutière, Frédéric 2 Priuli, Fabio Simone 1 Ackleh, Azmy S. 1 Aggarwal, Aekta 1 Amorim, Paulo 1 Bayen, Alexandre M. 1 Calvo, Daniela 1 Carrillo de la Plata, José Antonio 1 Cattani, Anna 1 Chyba, Monique 1 Crippa, Gianluca 1 De Lellis, Camillo 1 Facchi, Giancarlo 1 Frid, Hermano 1 Fryszkowski, Andrzej 1 Gokieli, Maria 1 Hille, Sander Cornelis 1 Křivan, Vlastimil 1 Kröner, Dietmar 1 Lorenz, Thomas 1 Maternini, Giulio 1 Mauri, Cristina 1 Meltzer, Marie-Christine 1 Meurer, Anne 1 Montanari, Annamaria 1 Muntean, Adrian 1 Nguyen, Khai T. 1 Pedretti, S. 1 Rascle, Michel 1 Risebro, Nils Henrik 1 Rosińska, Magdalena 1 Rzezuchowski, Tadeusz 1 Sachers, Veronika 1 Shen, Wen 1 Staicu, Vasile 1 Tandy, Matthew 1 Teixeira, Andreia Sofia 1 Trivisa, Konstantina 1 Ulikowska, Agnieszka all top 5 Serials 9 Journal of Differential Equations 8 Networks and Heterogeneous Media 5 Mathematical Methods in the Applied Sciences 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 SIAM Journal on Mathematical Analysis 4 Discrete and Continuous Dynamical Systems 4 Nonlinear Analysis. Real World Applications 4 Communications in Mathematical Sciences 4 Journal of Hyperbolic Differential Equations 4 Mathematical Biosciences and Engineering 4 Oberwolfach Reports 3 Journal of Mathematical Analysis and Applications 3 Quarterly of Applied Mathematics 3 Communications in Partial Differential Equations 3 SIAM Journal on Applied Mathematics 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Rivista di Matematica della Università di Parma. New Series 2 Archive for Rational Mechanics and Analysis 2 IMA Journal of Applied Mathematics 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Rendiconti del Seminario Matematico della Università di Padova 2 SIAM Journal on Control and Optimization 2 Applied Mathematics Letters 2 Mathematical and Computer Modelling 2 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Journal of Nonlinear Science 2 NoDEA. Nonlinear Differential Equations and Applications 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Acta Mathematica Scientia. Series B. (English Edition) 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Communications on Pure and Applied Analysis 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Communications in Mathematical Physics 1 Nonlinearity 1 Rocky Mountain Journal of Mathematics 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Applied Mathematics and Optimization 1 Funkcialaj Ekvacioj. Serio Internacia 1 Indiana University Mathematics Journal 1 Journal of Optimization Theory and Applications 1 Proceedings of the American Mathematical Society 1 Semigroup Forum 1 SIAM Journal on Numerical Analysis 1 Studies in Applied Mathematics 1 Rendiconti del Seminario Matematico 1 IMA Journal of Mathematics Applied in Medicine and Biology 1 European Journal of Applied Mathematics 1 Applications of Mathematics 1 Applied Mathematical Modelling 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Bulletin of the Polish Academy of Sciences, Mathematics 1 Continuum Mechanics and Thermodynamics 1 Calculus of Variations and Partial Differential Equations 1 Journal of Mathematical Sciences (New York) 1 Bollettino della Unione Matematica Italiana. Serie VIII. Sezione B. Articoli di Ricerca Matematica 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Interfaces and Free Boundaries 1 Flow, Turbulence and Combustion 1 Journal of Evolution Equations 1 Discrete and Continuous Dynamical Systems. Series B 1 Bulletin of the Brazilian Mathematical Society. New Series 1 SIAM Journal on Applied Dynamical Systems 1 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 1 Lecture Notes of the Unione Matematica Italiana 1 PAMM. Proceedings in Applied Mathematics and Mechanics 1 Discrete and Continuous Dynamical Systems. Series S 1 Journal of Mathematics in Industry all top 5 Fields 136 Partial differential equations (35-XX) 41 Operations research, mathematical programming (90-XX) 28 Fluid mechanics (76-XX) 18 Biology and other natural sciences (92-XX) 15 Ordinary differential equations (34-XX) 11 General and overarching topics; collections (00-XX) 10 Calculus of variations and optimal control; optimization (49-XX) 7 Numerical analysis (65-XX) 6 Operator theory (47-XX) 6 Mechanics of deformable solids (74-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Systems theory; control (93-XX) 4 Classical thermodynamics, heat transfer (80-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Measure and integration (28-XX) 3 General topology (54-XX) 1 Combinatorics (05-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Probability theory and stochastic processes (60-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 129 Publications have been cited 1,779 times in 865 Documents Cited by ▼ Year ▼ A class of nonlocal models for pedestrian traffic. Zbl 1248.35213 Colombo, Rinaldo M.; Garavello, Mauro; Lécureux-Mercier, Magali 106 2012 Hyperbolic phase transitions in traffic flow. Zbl 1037.35043 Colombo, Rinaldo M. 64 2002 Control of the continuity equation with a non local flow. Zbl 1232.35176 Colombo, Rinaldo M.; Herty, Michael; Mercier, Magali 64 2011 Pedestrian flows and non-classical shocks. Zbl 1108.90016 Colombo, Rinaldo M.; Rosini, Massimiliano D. 59 2005 Nonlocal crowd dynamics models for several populations. Zbl 1265.35214 Colombo, Rinaldo M.; Lécureux-Mercier, Magali 59 2012 An \(n\)-populations model for traffic flow. Zbl 1143.82323 Benzoni-Gavage, Sylvie; Colombo, Rinaldo M. 53 2003 The semigroup generated by \(2 \times 2\) conservation laws. Zbl 0849.35068 Bressan, Alberto; Colombo, Rinaldo M. 50 1995 Nonlocal systems of conservation laws in several space dimensions. Zbl 1318.65046 Aggarwal, Aekta; Colombo, Rinaldo M.; Goatin, Paola 47 2015 On the numerical integration of scalar nonlocal conservation laws. Zbl 1317.65165 Amorim, Paulo; Colombo, Rinaldo M.; Teixeira, Andreia 47 2015 Structured populations, cell growth and measure valued balance laws. Zbl 1250.47080 Carrillo, J. A.; Colombo, R. M.; Gwiazda, P.; Ulikowska, A. 42 2012 A well posed Riemann problem for the \(p\)-system at a junction. Zbl 1116.35086 Colombo, Rinaldo M.; Garavello, Mauro 40 2006 Optimal control in networks of pipes and canals. Zbl 1196.35135 Colombo, R. M.; Guerra, G.; Herty, M.; Schleper, V. 39 2009 On the Cauchy problem for the \(p\)-system at a junction. Zbl 1155.35399 Colombo, Rinaldo M.; Garavello, Mauro 35 2008 On \(2\times2\) conservation laws at a junction. Zbl 1171.35430 Colombo, R. M.; Herty, M.; Sachers, V. 34 2008 Continuous dependence for \(2 \times 2\) conservation laws with boundary. Zbl 0884.35091 Amadori, Debora; Colombo, Rinaldo M. 29 1997 Mixed systems: ODEs-balance laws. Zbl 1252.35193 Borsche, Raul; Colombo, Rinaldo M.; Garavello, Mauro 29 2012 A well posed conservation law with a variable unilateral constraint. Zbl 1116.35087 Colombo, Rinaldo M.; Goatin, Paola 29 2007 Stability and total variation estimates on general scalar balance laws. Zbl 1183.35197 Colombo, Rinaldo M.; Mercier, Magali; Rosini, Massimiliano D. 27 2009 A 2-phase traffic model based on a speed bound. Zbl 1211.35183 Colombo, Rinaldo M.; Marcellini, Francesca; Rascle, Michel 27 2010 A \(2\times 2\) hyperbolic traffic flow model. Zbl 0994.90021 Colombo, R. M. 25 2002 On the stability of the standard Riemann semigroup. Zbl 1026.35073 Bianchini, Stefano; Colombo, Rinaldo M. 25 2002 Unique solutions of \(2\times 2\) conservation laws with large data. Zbl 0852.35092 Bressan, Alberto; Colombo, Rinaldo M. 25 1995 On the modelling and management of traffic. Zbl 1267.90032 Colombo, Rinaldo M.; Goatin, Paola; Rosini, Massimiliano D. 25 2011 On the coupling of systems of hyperbolic conservation laws with ordinary differential equations. Zbl 1205.35170 Borsche, Raul; Colombo, Rinaldo M.; Garavello, Mauro 23 2010 Continuous selections of solution sets of Lipschitzean differential inclusions. Zbl 0749.34008 Colombo, R. M.; Fryszkowski, A.; Rzežuchowski, T.; Staicu, V. 21 1991 Existence of nonclassical solutions in a pedestrian flow model. Zbl 1169.35360 Colombo, Rinaldo M.; Rosini, Massimiliano D. 20 2009 On general balance laws with boundary. Zbl 1196.35136 Colombo, Rinaldo M.; Guerra, Graziano 20 2010 Selective strategies in food webs. Zbl 0807.92025 Colombo, Rinaldo M.; Křivan, Vlastimil 19 1993 Continuous dependence in conservation laws with phase transitions. Zbl 0977.35085 Colombo, Rinaldo M.; Corli, Andrea 18 1999 A Hölder continuous ODE related to traffic flow. Zbl 1052.34007 Colombo, Rinaldo M.; Marson, Andrea 18 2003 Differential equations in metric spaces with applications. Zbl 1171.34040 Colombo, Rinaldo M.; Guerra, Graziano 18 2009 Euler system for compressible fluids at a junction. Zbl 1168.35029 Colombo, Rinaldo M.; Mauri, Cristina 18 2008 An age and space structured SIR model describing the covid-19 pandemic. Zbl 1469.92107 Colombo, Rinaldo M.; Garavello, Mauro; Marcellini, Francesca; Rossi, Elena 18 2020 Hyperbolic balance laws with a non local source. Zbl 1138.35059 Colombo, Rinaldo M.; Guerra, Graziano 17 2007 On the control of moving sets: positive and negative confinement results. Zbl 1279.34074 Colombo, R. M.; Pogodaev, N. 16 2013 Nonlocal conservation laws in bounded domains. Zbl 1395.35143 Colombo, Rinaldo M.; Rossi, Elena 15 2018 On the micro-macro limit in traffic flow. Zbl 1295.35314 Colombo, R. M.; Rossi, E. 15 2014 Decay of positive waves in nonlinear systems of conservation laws. Zbl 0906.35059 Bressan, Alberto; Colombo, Rinaldo M. 15 1998 Road networks with phase transitions. Zbl 1189.35176 Colombo, Rinaldo M.; Goatin, Paola; Piccoli, Benedetto 15 2010 An analytical framework to describe the interactions between individuals and a continuum. Zbl 1241.35208 Colombo, Rinaldo M.; Lécureux-Mercier, Magali 14 2012 Rigorous estimates on balance laws in bounded domains. Zbl 1340.35202 Colombo, Rinaldo M.; Rossi, Elena 13 2015 On the modeling of moving populations through set evolution equations. Zbl 1311.34035 Colombo, Rinaldo M.; Lorenz, Thomas; Pogodaev, Nikolay I. 13 2015 Hyperbolic predators vs. parabolic prey. Zbl 1315.35062 Colombo, Rinaldo M.; Rossi, Elena 13 2015 A mixed ODE-PDE model for vehicular traffic. Zbl 1320.35209 Colombo, Rinaldo M.; Marcellini, Francesca 13 2015 Confinement strategies in a model for the interaction between individuals and a continuum. Zbl 1258.34038 Colombo, R. M.; Pogodaev, N. 13 2012 On the role of source terms in continuum traffic flow models. Zbl 1145.35426 Bagnerini, Patrizia; Colombo, Rinaldo M.; Corli, Andrea 13 2006 Nonlocal systems of balance laws in several space dimensions with applications to laser technology. Zbl 1327.35245 Colombo, Rinaldo M.; Marcellini, Francesca 12 2015 Continuous dependence in the large for some equations of gas dynamics. Zbl 0927.35082 Colombo, Rinaldo M.; Risebro, Nils H. 12 1998 On a class of hyperbolic balance laws. Zbl 1066.35055 Colombo, Rinaldo M.; Corli, Andrea 12 2004 Global well posedness of traffic flow models with phase transitions. Zbl 1113.35123 Colombo, Rinaldo M.; Goatin, Paola; Priuli, Fabio S. 12 2007 Differential equations modeling crowd interactions. Zbl 1327.35244 Borsche, Raul; Colombo, Rinaldo M.; Garavello, Mauro; Meurer, Anne 11 2015 Viscosity solutions and standard Riemann semigroup for conservation laws with boundary. Zbl 0910.35078 Amadori, Debora; Colombo, Rinaldo M. 11 1998 Minimising stop and go waves to optimise traffic flow. Zbl 1058.49011 Colombo, R. M.; Groli, A. 11 2004 A macroscopic model for pedestrian flows in panic situations. Zbl 1226.35050 Colombo, Rinaldo M.; Goatin, Paola; Rosini, Massimiliano D. 11 2010 A semilinear structure on semigroups in a metric space. Zbl 1069.47065 Colombo, Rinaldo M.; Corli, Andrea 10 2004 The compressible to incompressible limit of one dimensional Euler equations: the non smooth case. Zbl 1333.35169 Colombo, Rinaldo M.; Guerra, Graziano; Schleper, Veronika 10 2016 Hyperbolic balance laws with a dissipative non local source. Zbl 1151.35398 Colombo, Rinaldo M.; Guerra, Graziano 10 2008 Biological and industrial models motivating nonlocal conservation laws: a review of analytic and numerical results. Zbl 1350.35114 Colombo, Rinaldo M.; Marcellini, Francesca; Rossi, Elena 8 2016 Well posedness of balance laws with boundary. Zbl 1079.35061 Colombo, Rinaldo M.; Rosini, Massimiliano D. 8 2005 Non-local crowd dynamics. Zbl 1225.35053 Colombo, Rinaldo M.; Garavello, Mauro; Lécureux-Mercier, Magali 8 2011 Non local balance laws in traffic models and crystal growth. Zbl 1117.35321 Colombo, Rinaldo M.; Corli, Andrea; Rosini, Massimiliano D. 8 2007 Well posedness and control in a nonlocal SIR model. Zbl 1470.35232 Colombo, Rinaldo M.; Garavello, Mauro 8 2021 On the initial boundary value problem for Temple systems. Zbl 1058.35150 Colombo, Rinaldo M.; Groli, Alessandro 7 2004 Initial data identification in conservation laws and Hamilton-Jacobi equations. Zbl 1439.35128 Colombo, Rinaldo M.; Perrollaz, Vincent 7 2020 On the \(p\)-system at a junction. Zbl 1128.35071 Colombo, Rinaldo M.; Garavello, Mauro 7 2007 Characterization of Riemann solvers for the two phase \(p\)-system. Zbl 1030.35117 Colombo, Rinaldo M.; Priuli, Fabio S. 7 2003 Two-phase flows: non-smooth well posedness and the compressible to incompressible limit. Zbl 1254.76119 Colombo, Rinaldo M.; Schleper, Veronika 7 2012 Optimizing vaccination strategies in an age structured SIR model. Zbl 1470.92185 Colombo, Rinaldo M.; Garavello, Mauro 7 2020 A traffic model aware of real time data. Zbl 1339.35176 Colombo, Rinaldo M.; Marcellini, Francesca 6 2016 On the interactions between a solid body and a compressible inviscid fluid. Zbl 1286.35159 Borsche, Raul; Colombo, Rinaldo M.; Garavello, Mauro 6 2013 BV solutions to 1D isentropic Euler equations in the zero Mach number limit. Zbl 1359.35139 Colombo, Rinaldo M.; Guerra, Graziano 6 2016 Sonic and kinetic phase transitions with applications to Chapman-Jouguet deflagrations. Zbl 1047.35096 Colombo, Rinaldo M.; Corli, Andrea 6 2004 Modelling the dynamics of granular matter. Zbl 1251.35068 Colombo, Rinaldo M.; Guerra, Graziano; Monti, Francesca 6 2012 Smooth and discontinuous junctions in the \(p\)-system. Zbl 1421.76141 Colombo, Rinaldo M.; Marcellini, Francesca 6 2010 Stability and optimization in structured population models on graphs. Zbl 1320.92068 Colombo, Rinaldo M.; Garavello, Mauro 6 2015 Well posedness for multilane traffic models. Zbl 1138.35361 Colombo, Rinaldo M.; Corli, Andrea 6 2006 On the stability functional for conservation laws. Zbl 1157.35423 Colombo, Rinaldo M.; Guerra, Graziano 6 2008 Sonic hyperbolic phase transitions and Chapman-Jouguet detonations. Zbl 1024.35070 Colombo, Rinaldo M.; Corli, Andrea 5 2002 Wave front tracking in systems of conservation laws. Zbl 1099.35063 Colombo, Rinaldo M. 5 2004 Phase transitions in hyperbolic conservation laws. Zbl 1060.35523 Colombo, Rinaldo M. 5 2003 \(L^{1}\) stability of spatially periodic solutions in relativistic gas dynamics. Zbl 1168.35044 Calvo, Daniela; Colombo, Rinaldo M.; Frid, Hermano 5 2008 Modelling crowd movements in domains with boundaries. Zbl 1427.91190 Colombo, Rinaldo M.; Rossi, Elena 5 2019 A hyperbolic model for the laser cutting process. Zbl 1426.74245 Colombo, R. M.; Guerra, G.; Herty, M.; Marcellini, F. 5 2013 \(2 \times 2\) systems of conservation laws with \(L^{\infty }\) data. Zbl 1213.35301 Bianchini, Stefano; Colombo, Rinaldo M.; Monti, Francesca 5 2010 Coupling conditions for the \(3 \times 3\) Euler system. Zbl 1284.35328 Colombo, Rinaldo M.; Marcellini, Francesca 5 2010 Transport equations and multi-D hyperbolic conservation laws. Zbl 1131.35300 5 2008 Measure valued solutions to conservation laws motivated by traffic modelling. Zbl 1149.35386 Benzoni-Gavage, Sylvie; Colombo, Rinaldo M.; Gwiazda, Piotr 5 2006 Comparison among different notions of solution for the \(p\)-system at a junction. Zbl 1188.35114 Colombo, Rinaldo M.; Garavello, Mauro 5 2009 Control of biological resources on graphs. Zbl 1372.35306 Colombo, Rinaldo M.; Garavello, Mauro 4 2017 On the optimization of the initial boundary value problem for a conservation law. Zbl 1041.35037 Colombo, Rinaldo M.; Groli, Alessandro 4 2004 Lipschitz semigroup for an integro-differential equation for slow erosion. Zbl 1250.35175 Colombo, Rinaldo M.; Guerra, Graziano; Shen, Wen 4 2012 Stability estimates on general scalar balance laws. Zbl 1160.35473 Colombo, Rinaldo M.; Mercier, Magali; Rosini, Massimiliano D. 4 2009 Modeling crowd dynamics through hyperbolic-elliptic equations. Zbl 1402.35080 Colombo, Rinaldo M.; Gokieli, Maria; Rosini, Massimiliano D. 4 2018 On the Braess paradox with nonlinear dynamics and control theory. Zbl 1335.35154 Colombo, Rinaldo M.; Holden, Helge 4 2016 Conservation laws with unilateral constraints in traffic modeling. Zbl 1211.35182 Colombo, Rinaldo M.; Goatin, Paola; Rosini, Massimiliano D. 4 2010 Traffic flow models with phase transitions. Zbl 1134.90012 Colombo, Rinaldo M.; Goatin, Paola 4 2006 A modeling framework for biological pest control. Zbl 1470.92392 Colombo, Rinaldo M.; Rossi, Elena 4 2020 IBVPs for scalar conservation laws with time discontinuous fluxes. Zbl 1400.35179 Colombo, Rinaldo M.; Rossi, Elena 3 2018 Conservation versus balance laws in traffic flows. Zbl 1137.90392 Bagnerini, P.; Colombo, R. M.; Corli, A.; Pedretti, S. 3 2005 A multispecies traffic model based on the Lighthill-Whitham and Richards model. Zbl 1409.35138 Colombo, Rinaldo M.; Klingenberg, Christian; Meltzer, Marie-Christine 3 2018 Conservation laws and Hamilton-Jacobi equations with space inhomogeneity. Zbl 1518.35228 Colombo, Rinaldo M.; Perrollaz, Vincent; Sylla, Abraham 3 2023 Examples and conjectures on the regularity of solutions to balance laws. Zbl 1517.35134 Ancona, Fabio; Bianchini, Stefano; Bressan, Alberto; Colombo, Rinaldo M.; Nguyen, Khai T. 1 2023 Vaccination strategies through intra-compartmental dynamics. Zbl 1501.92084 Colombo, Rinaldo M.; Marcellini, Francesca; Rossi, Elena 1 2022 Advanced mathematical methodologies to contrast COVID-19 pandemic. Zbl 07607846 1 2022 Well posedness and control in a nonlocal SIR model. Zbl 1470.35232 Colombo, Rinaldo M.; Garavello, Mauro 8 2021 Well-posedness and control in a hyperbolic-parabolic parasitoid-parasite system. Zbl 1476.35101 Colombo, Rinaldo M.; Rossi, Elena 1 2021 An age and space structured SIR model describing the covid-19 pandemic. Zbl 1469.92107 Colombo, Rinaldo M.; Garavello, Mauro; Marcellini, Francesca; Rossi, Elena 18 2020 Initial data identification in conservation laws and Hamilton-Jacobi equations. Zbl 1439.35128 Colombo, Rinaldo M.; Perrollaz, Vincent 7 2020 Optimizing vaccination strategies in an age structured SIR model. Zbl 1470.92185 Colombo, Rinaldo M.; Garavello, Mauro 7 2020 A modeling framework for biological pest control. Zbl 1470.92392 Colombo, Rinaldo M.; Rossi, Elena 4 2020 Special issue: Mathematical modeling with measures. Zbl 1477.00013 3 2020 Crowd dynamics through conservation laws. Zbl 1471.90051 Colombo, Rinaldo M.; Lecureux-Mercier, Magali; Garavello, Mauro 2 2020 On the microscopic modeling of vehicular traffic on general networks. Zbl 1448.90034 Colombo, Rinaldo M.; Holden, Helge; Marcellini, Francesca 2 2020 On the 1D modeling of fluid flowing through a junction. Zbl 1452.35138 Colombo, Rinaldo M.; Garavello, Mauro 2 2020 Modelling crowd movements in domains with boundaries. Zbl 1427.91190 Colombo, Rinaldo M.; Rossi, Elena 5 2019 Stability of the 1D IBVP for a non autonomous scalar conservation law. Zbl 1447.35217 Colombo, Rinaldo M.; Rossi, Elena 3 2019 Hyperbolic consensus games. Zbl 1426.35154 Colombo, Rinaldo M.; Garavello, Mauro 2 2019 Nonlocal conservation laws in bounded domains. Zbl 1395.35143 Colombo, Rinaldo M.; Rossi, Elena 15 2018 Modeling crowd dynamics through hyperbolic-elliptic equations. Zbl 1402.35080 Colombo, Rinaldo M.; Gokieli, Maria; Rosini, Massimiliano D. 4 2018 IBVPs for scalar conservation laws with time discontinuous fluxes. Zbl 1400.35179 Colombo, Rinaldo M.; Rossi, Elena 3 2018 A multispecies traffic model based on the Lighthill-Whitham and Richards model. Zbl 1409.35138 Colombo, Rinaldo M.; Klingenberg, Christian; Meltzer, Marie-Christine 3 2018 Optimization in structure population models through the escalator boxcar train. Zbl 1407.65237 Colombo, Rinaldo M.; Gwiazda, Piotr; Rosińska, Magdalena 1 2018 Control of biological resources on graphs. Zbl 1372.35306 Colombo, Rinaldo M.; Garavello, Mauro 4 2017 The compressible to incompressible limit of one dimensional Euler equations: the non smooth case. Zbl 1333.35169 Colombo, Rinaldo M.; Guerra, Graziano; Schleper, Veronika 10 2016 Biological and industrial models motivating nonlocal conservation laws: a review of analytic and numerical results. Zbl 1350.35114 Colombo, Rinaldo M.; Marcellini, Francesca; Rossi, Elena 8 2016 A traffic model aware of real time data. Zbl 1339.35176 Colombo, Rinaldo M.; Marcellini, Francesca 6 2016 BV solutions to 1D isentropic Euler equations in the zero Mach number limit. Zbl 1359.35139 Colombo, Rinaldo M.; Guerra, Graziano 6 2016 On the Braess paradox with nonlinear dynamics and control theory. Zbl 1335.35154 Colombo, Rinaldo M.; Holden, Helge 4 2016 Isentropic fluid dynamics in a curved pipe. Zbl 1362.35182 Colombo, Rinaldo M.; Holden, Helge 3 2016 A coupling between a non-linear 1D compressible-incompressible limit and the 1D \(p\)-system in the non smooth case. Zbl 1342.35232 Guerra, Graziano; Colombo, Rinaldo M. 3 2016 Characterization of the solutions to ODE-PDE systems. Zbl 1348.35135 Colombo, Rinaldo M.; Guerra, Graziano 2 2016 Nonlocal systems of conservation laws in several space dimensions. Zbl 1318.65046 Aggarwal, Aekta; Colombo, Rinaldo M.; Goatin, Paola 47 2015 On the numerical integration of scalar nonlocal conservation laws. Zbl 1317.65165 Amorim, Paulo; Colombo, Rinaldo M.; Teixeira, Andreia 47 2015 Rigorous estimates on balance laws in bounded domains. Zbl 1340.35202 Colombo, Rinaldo M.; Rossi, Elena 13 2015 On the modeling of moving populations through set evolution equations. Zbl 1311.34035 Colombo, Rinaldo M.; Lorenz, Thomas; Pogodaev, Nikolay I. 13 2015 Hyperbolic predators vs. parabolic prey. Zbl 1315.35062 Colombo, Rinaldo M.; Rossi, Elena 13 2015 A mixed ODE-PDE model for vehicular traffic. Zbl 1320.35209 Colombo, Rinaldo M.; Marcellini, Francesca 13 2015 Nonlocal systems of balance laws in several space dimensions with applications to laser technology. Zbl 1327.35245 Colombo, Rinaldo M.; Marcellini, Francesca 12 2015 Differential equations modeling crowd interactions. Zbl 1327.35244 Borsche, Raul; Colombo, Rinaldo M.; Garavello, Mauro; Meurer, Anne 11 2015 Stability and optimization in structured population models on graphs. Zbl 1320.92068 Colombo, Rinaldo M.; Garavello, Mauro 6 2015 On the micro-macro limit in traffic flow. Zbl 1295.35314 Colombo, R. M.; Rossi, E. 15 2014 Phase transition model for traffic at a junction. Zbl 1305.90107 Colombo, R. M.; Garavello, M. 3 2014 On the control of moving sets: positive and negative confinement results. Zbl 1279.34074 Colombo, R. M.; Pogodaev, N. 16 2013 On the interactions between a solid body and a compressible inviscid fluid. Zbl 1286.35159 Borsche, Raul; Colombo, Rinaldo M.; Garavello, Mauro 6 2013 A hyperbolic model for the laser cutting process. Zbl 1426.74245 Colombo, R. M.; Guerra, G.; Herty, M.; Marcellini, F. 5 2013 A class of nonlocal models for pedestrian traffic. Zbl 1248.35213 Colombo, Rinaldo M.; Garavello, Mauro; Lécureux-Mercier, Magali 106 2012 Nonlocal crowd dynamics models for several populations. Zbl 1265.35214 Colombo, Rinaldo M.; Lécureux-Mercier, Magali 59 2012 Structured populations, cell growth and measure valued balance laws. Zbl 1250.47080 Carrillo, J. A.; Colombo, R. M.; Gwiazda, P.; Ulikowska, A. 42 2012 Mixed systems: ODEs-balance laws. Zbl 1252.35193 Borsche, Raul; Colombo, Rinaldo M.; Garavello, Mauro 29 2012 An analytical framework to describe the interactions between individuals and a continuum. Zbl 1241.35208 Colombo, Rinaldo M.; Lécureux-Mercier, Magali 14 2012 Confinement strategies in a model for the interaction between individuals and a continuum. Zbl 1258.34038 Colombo, R. M.; Pogodaev, N. 13 2012 Two-phase flows: non-smooth well posedness and the compressible to incompressible limit. Zbl 1254.76119 Colombo, Rinaldo M.; Schleper, Veronika 7 2012 Modelling the dynamics of granular matter. Zbl 1251.35068 Colombo, Rinaldo M.; Guerra, Graziano; Monti, Francesca 6 2012 Lipschitz semigroup for an integro-differential equation for slow erosion. Zbl 1250.35175 Colombo, Rinaldo M.; Guerra, Graziano; Shen, Wen 4 2012 Control of the continuity equation with a non local flow. Zbl 1232.35176 Colombo, Rinaldo M.; Herty, Michael; Mercier, Magali 64 2011 On the modelling and management of traffic. Zbl 1267.90032 Colombo, Rinaldo M.; Goatin, Paola; Rosini, Massimiliano D. 25 2011 Non-local crowd dynamics. Zbl 1225.35053 Colombo, Rinaldo M.; Garavello, Mauro; Lécureux-Mercier, Magali 8 2011 Well posedness and control in models based on conservation laws. Zbl 1248.35120 Colombo, Rinaldo M. 3 2011 A 2-phase traffic model based on a speed bound. Zbl 1211.35183 Colombo, Rinaldo M.; Marcellini, Francesca; Rascle, Michel 27 2010 On the coupling of systems of hyperbolic conservation laws with ordinary differential equations. Zbl 1205.35170 Borsche, Raul; Colombo, Rinaldo M.; Garavello, Mauro 23 2010 On general balance laws with boundary. Zbl 1196.35136 Colombo, Rinaldo M.; Guerra, Graziano 20 2010 Road networks with phase transitions. Zbl 1189.35176 Colombo, Rinaldo M.; Goatin, Paola; Piccoli, Benedetto 15 2010 A macroscopic model for pedestrian flows in panic situations. Zbl 1226.35050 Colombo, Rinaldo M.; Goatin, Paola; Rosini, Massimiliano D. 11 2010 Smooth and discontinuous junctions in the \(p\)-system. Zbl 1421.76141 Colombo, Rinaldo M.; Marcellini, Francesca 6 2010 \(2 \times 2\) systems of conservation laws with \(L^{\infty }\) data. Zbl 1213.35301 Bianchini, Stefano; Colombo, Rinaldo M.; Monti, Francesca 5 2010 Coupling conditions for the \(3 \times 3\) Euler system. Zbl 1284.35328 Colombo, Rinaldo M.; Marcellini, Francesca 5 2010 Conservation laws with unilateral constraints in traffic modeling. Zbl 1211.35182 Colombo, Rinaldo M.; Goatin, Paola; Rosini, Massimiliano D. 4 2010 \(L^\infty\) solutions for \(2\times 2\) systems of conservation laws. Zbl 1223.35225 Bianchini, S.; Colombo, R. M.; Monti, F. 1 2010 Optimal control in networks of pipes and canals. Zbl 1196.35135 Colombo, R. M.; Guerra, G.; Herty, M.; Schleper, V. 39 2009 Stability and total variation estimates on general scalar balance laws. Zbl 1183.35197 Colombo, Rinaldo M.; Mercier, Magali; Rosini, Massimiliano D. 27 2009 Existence of nonclassical solutions in a pedestrian flow model. Zbl 1169.35360 Colombo, Rinaldo M.; Rosini, Massimiliano D. 20 2009 Differential equations in metric spaces with applications. Zbl 1171.34040 Colombo, Rinaldo M.; Guerra, Graziano 18 2009 Comparison among different notions of solution for the \(p\)-system at a junction. Zbl 1188.35114 Colombo, Rinaldo M.; Garavello, Mauro 5 2009 Stability estimates on general scalar balance laws. Zbl 1160.35473 Colombo, Rinaldo M.; Mercier, Magali; Rosini, Massimiliano D. 4 2009 On the continuum modeling of crowds. Zbl 1190.35149 Colombo, Rinaldo M.; Facchi, Giancarlo; Maternini, Giulio; Rosini, Massimiliano D. 3 2009 Balance laws as quasidifferential equations in metric spaces. Zbl 1190.35150 Colombo, Rinaldo M.; Guerra, Graziano 3 2009 On the Cauchy problem for the \(p\)-system at a junction. Zbl 1155.35399 Colombo, Rinaldo M.; Garavello, Mauro 35 2008 On \(2\times2\) conservation laws at a junction. Zbl 1171.35430 Colombo, R. M.; Herty, M.; Sachers, V. 34 2008 Euler system for compressible fluids at a junction. Zbl 1168.35029 Colombo, Rinaldo M.; Mauri, Cristina 18 2008 Hyperbolic balance laws with a dissipative non local source. Zbl 1151.35398 Colombo, Rinaldo M.; Guerra, Graziano 10 2008 On the stability functional for conservation laws. Zbl 1157.35423 Colombo, Rinaldo M.; Guerra, Graziano 6 2008 \(L^{1}\) stability of spatially periodic solutions in relativistic gas dynamics. Zbl 1168.35044 Calvo, Daniela; Colombo, Rinaldo M.; Frid, Hermano 5 2008 Transport equations and multi-D hyperbolic conservation laws. Zbl 1131.35300 5 2008 Nonlocal sources in hyperbolic balance laws with applications. Zbl 1140.35517 Colombo, R. M.; Guerra, G. 3 2008 Mini-workshop: Hyperbolic aspects of phase transition dynamics. Abstracts from the mini-workshop held February 24 – March 1, 2008. Zbl 1177.35008 1 2008 A well posed conservation law with a variable unilateral constraint. Zbl 1116.35087 Colombo, Rinaldo M.; Goatin, Paola 29 2007 Hyperbolic balance laws with a non local source. Zbl 1138.35059 Colombo, Rinaldo M.; Guerra, Graziano 17 2007 Global well posedness of traffic flow models with phase transitions. Zbl 1113.35123 Colombo, Rinaldo M.; Goatin, Paola; Priuli, Fabio S. 12 2007 Non local balance laws in traffic models and crystal growth. Zbl 1117.35321 Colombo, Rinaldo M.; Corli, Andrea; Rosini, Massimiliano D. 8 2007 On the \(p\)-system at a junction. Zbl 1128.35071 Colombo, Rinaldo M.; Garavello, Mauro 7 2007 Well posedness of balance laws with non-characteristic boundary. Zbl 1180.35341 Colombo, Rinaldo M.; Rosini, Massimiliano D. 3 2007 On the operator splitting method: nonlinear balance laws and a generalization of Trotter-Kato formulas. Zbl 1123.35028 Colombo, Rinaldo M.; Corli, Andrea 1 2007 A well posed Riemann problem for the \(p\)-system at a junction. Zbl 1116.35086 Colombo, Rinaldo M.; Garavello, Mauro 40 2006 On the role of source terms in continuum traffic flow models. Zbl 1145.35426 Bagnerini, Patrizia; Colombo, Rinaldo M.; Corli, Andrea 13 2006 Well posedness for multilane traffic models. Zbl 1138.35361 Colombo, Rinaldo M.; Corli, Andrea 6 2006 Measure valued solutions to conservation laws motivated by traffic modelling. Zbl 1149.35386 Benzoni-Gavage, Sylvie; Colombo, Rinaldo M.; Gwiazda, Piotr 5 2006 Traffic flow models with phase transitions. Zbl 1134.90012 Colombo, Rinaldo M.; Goatin, Paola 4 2006 Pedestrian flows and non-classical shocks. Zbl 1108.90016 Colombo, Rinaldo M.; Rosini, Massimiliano D. 59 2005 Well posedness of balance laws with boundary. Zbl 1079.35061 Colombo, Rinaldo M.; Rosini, Massimiliano D. 8 2005 Conservation versus balance laws in traffic flows. Zbl 1137.90392 Bagnerini, P.; Colombo, R. M.; Corli, A.; Pedretti, S. 3 2005 ...and 29 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 941 Authors 77 Colombo, Rinaldo M. 46 Goatin, Paola 37 Garavello, Mauro 34 Herty, Michael Matthias 32 Piccoli, Benedetto 28 Rosini, Massimiliano Daniele 27 Göttlich, Simone 23 Bressan, Alberto 21 Coclite, Giuseppe Maria 20 Bürger, Raimund 19 Corli, Andrea 19 Marcellini, Francesca 18 Andreianov, Boris 18 Rossi, Elena 18 Tosin, Andrea 17 Borsche, Raul 17 Guerra, Graziano 17 Gwiazda, Piotr 17 Keimer, Alexander 14 Amadori, Debora 14 Gugat, Martin 14 Pflug, Lukas 14 Shen, Wen 13 Klar, Axel 13 Křivan, Vlastimil 13 Villada, Luis Miguel 12 Donadello, Carlotta 11 Chiarello, Felisia Angela 10 Cristiani, Emiliano 10 Pareschi, Lorenzo 9 Ancona, Fabio 9 Holden, Helge 9 Lorenz, Thomas 9 Mulet, Pep 9 Pogodaev, Nikolaĭ Il’ich 9 Schleper, Veronika 9 Spinolo, Laura V. 8 Chalons, Christophe 8 Delle Monache, Maria Laura 8 Friedrich, Jan 8 Leugering, Günter 8 Marciniak-Czochra, Anna K. 8 Wolfram, Marie-Therese 8 Zuazua, Enrique 7 Albi, Giacomo 7 Berthelin, Florent 7 Bianchini, Stefano 7 Briani, Maya 7 De Nitti, Nicola 7 Kolb, Oliver 7 Lécureux-Mercier, Magali 7 Risebro, Nils Henrik 7 Rohde, Christian 7 Vauchelet, Nicolas 7 Zanella, Mattia 6 Banda, Mapundi Kondwani 6 Bertaglia, Giulia 6 Carrillo de la Plata, José Antonio 6 Crippa, Gianluca 6 Di Francesco, Marco 6 Di Ruvo, Lorenzo 6 Du, Qiang 6 Malaguti, Luisa 6 Sylla, Abraham 5 Ackleh, Azmy S. 5 Bellomo, Nicola 5 Chiri, Maria Teresa 5 Coron, Jean-Michel 5 Degond, Pierre 5 Fagioli, Simone 5 Fryszkowski, Andrzej 5 Hille, Sander Cornelis 5 Lagoutière, Frédéric 5 LeFloch, Philippe Gerard 5 Meurer, Anne 5 Razafison, Ulrich 5 Saintier, Nicolas 5 Tiwari, Sudarshan 5 Vega, Carlos A. 5 Yu, Lei 4 Aggarwal, Aekta 4 Bayen, Alexandre M. 4 Bermúdez, Alfredo 4 Caravenna, Laura 4 Chen, Gui-Qiang G. 4 Colombo, Maria 4 D’Apice, Ciro 4 Dimarco, Giacomo 4 Donat, Rosa 4 Fokken, Eike 4 Forcadel, Nicolas 4 Gabriel, Pierre 4 James, François 4 Lambert, Wanderson J. 4 Liard, Thibault 4 López, Xián 4 Müller, Siegfried 4 Nguyen, Khai T. 4 Quincampoix, Marc 4 Reigstad, Gunhild Allard ...and 841 more Authors all top 5 Cited in 190 Serials 55 Networks and Heterogeneous Media 54 Journal of Differential Equations 40 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 29 Journal of Hyperbolic Differential Equations 24 Journal of Mathematical Analysis and Applications 24 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 21 Archive for Rational Mechanics and Analysis 21 SIAM Journal on Applied Mathematics 19 SIAM Journal on Mathematical Analysis 18 Journal of Computational Physics 15 NoDEA. Nonlinear Differential Equations and Applications 15 Mathematical Biosciences and Engineering 15 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 13 ZAMP. Zeitschrift für angewandte Mathematik und Physik 13 Discrete and Continuous Dynamical Systems 12 SIAM Journal on Control and Optimization 10 Mathematical Methods in the Applied Sciences 10 Applied Mathematical Modelling 10 Nonlinear Analysis. Real World Applications 10 Bulletin of the Brazilian Mathematical Society. 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Analyse Non Linéaire 3 European Journal of Applied Mathematics 3 Applications of Mathematics 3 Journal of Dynamics and Differential Equations 3 Journal of Mathematical Sciences (New York) 3 Mathematical Problems in Engineering 3 Communications in Nonlinear Science and Numerical Simulation 3 Living Reviews in Relativity 3 Journal of Evolution Equations 3 Multiscale Modeling & Simulation 2 Physics Letters. A 2 Mathematics of Computation 2 Chaos, Solitons and Fractals 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 BIT 2 Rendiconti del Seminario Matematico della Università di Padova 2 Siberian Mathematical Journal 2 Acta Mathematicae Applicatae Sinica. English Series 2 MCSS. Mathematics of Control, Signals, and Systems 2 Journal of Nonlinear Science 2 Continuum Mechanics and Thermodynamics 2 Computational Optimization and Applications 2 Calculus of Variations and Partial Differential Equations 2 Advances in Computational Mathematics 2 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 2 Mathematical and Computer Modelling of Dynamical Systems 2 Optimization and Engineering 2 Set-Valued and Variational Analysis 2 Mathematical Control and Related Fields 2 Communications in Applied and Industrial Mathematics 2 ISRN Applied Mathematics 2 Evolution Equations and Control Theory 2 Journal of Computational Dynamics 2 Minimax Theory and its Applications 2 Annales Henri Lebesgue 2 SN Partial Differential Equations and Applications 2 Foundations of Data Science ...and 90 more Serials all top 5 Cited in 37 Fields 612 Partial differential equations (35-XX) 256 Operations research, mathematical programming (90-XX) 223 Fluid mechanics (76-XX) 171 Numerical analysis (65-XX) 101 Biology and other natural sciences (92-XX) 85 Systems theory; control (93-XX) 80 Calculus of variations and optimal control; optimization (49-XX) 58 Ordinary differential equations (34-XX) 43 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 41 Statistical mechanics, structure of matter (82-XX) 24 Probability theory and stochastic processes (60-XX) 22 Integral equations (45-XX) 22 Mechanics of deformable solids (74-XX) 18 Operator theory (47-XX) 14 Measure and integration (28-XX) 11 Dynamical systems and ergodic theory (37-XX) 8 Real functions (26-XX) 8 Statistics (62-XX) 7 General topology (54-XX) 7 Computer science (68-XX) 7 Optics, electromagnetic theory (78-XX) 7 Relativity and gravitational theory (83-XX) 6 Mechanics of particles and systems (70-XX) 5 Functional analysis (46-XX) 5 Global analysis, analysis on manifolds (58-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 Combinatorics (05-XX) 3 Quantum theory (81-XX) 3 Geophysics (86-XX) 2 General and overarching topics; collections (00-XX) 2 Approximations and expansions (41-XX) 2 Integral transforms, operational calculus (44-XX) 2 Astronomy and astrophysics (85-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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