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## Bellomo, Nicola

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 Author ID: bellomo.nicola Published as: Bellomo, N.; Bellomo, Nicola Homepage: http://staff.polito.it/nicola.bellomo/ External Links: MGP · dblp · GND
 Documents Indexed: 214 Publications since 1969, including 24 Books
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#### Co-Authors

 14 single-authored 25 Bellouquid, Abdelghani 16 Brezzi, Franco 13 Soler, Juan S. 11 Lachowicz, Mirosław 9 Gibelli, Livio 9 Riganti, Riccardo 8 De Angelis, Elena 8 Knopoff, Damian A. 8 Pistone, Giovanni 8 Preziosi, Luigi 8 Toscani, Giuseppe 7 Arlotti, Luisa 6 Monaco, Roberto 6 Nieto, Juanjo 6 Winkler, Michael 5 Coscia, Vincenzo 5 Delitala, Marcello 5 Fermo, Luisa 5 Longo, Eugenia 5 Polewczak, Jacek 5 Tao, Youshan 4 Bonzani, Ida 4 de Socio, Luciano M. 4 Loiodice, Rocco 4 Vacca, Maria Teresa 3 Aylaj, Bouchra 3 Bianca, Carlo 3 Carbonaro, Bruno 3 Forni, Guido 3 Ha, Seung-Yeal 3 Outada, Nisrine 3 Pulvirenti, Mario 3 Rizzi, Guido 3 Romano, Antonio Enea 3 Teppati, Giancarlo 3 Tosin, Andrea 2 Adomian, George 2 Ajmone Marsan, Giulia 2 Battaglio, M. 2 Berestycki, Henri 2 Bertotti, Maria Letizia 2 Chaplain, Mark A. J. 2 Chouhad, Nadia 2 De Lillo, Silvana 2 Degond, Pierre 2 Dogbé, Christian 2 Dosi, Giovanni 2 Gatignol, Renée 2 Herrero, Miguel Ángel 2 Lo Schiavo, Mauro 2 Maini, Philip Kumar 2 Mamontov, Eugen 2 Nadal, Jean-Pierre 2 Palczewski, Andrzej 2 Ridolfi, Luca 2 Tadmor, Eitan 2 Virgillito, Maria Enrica 2 Willander, Magnus 2 Zavattaro, M. G. 1 Adam, John A. 1 Albi, Giacomo 1 Ambrosi, Davide 1 Antonelli, Dario 1 Arnod, S. 1 Bellouquid, Abdel 1 Berrone, Stefano 1 Bingham, Richard 1 Bruno, Luca 1 Brzeźniak, Zdzisław 1 Cafaro, Emilio 1 Calander, Nils 1 Carloni, A. 1 Chilosi, M. 1 Colasuonno, Francesca 1 De Nigris, Sarah 1 Egidi, Massimo 1 Esteban, Maria J. 1 Firmani, Bruno 1 Flandoli, Franco 1 Formaggia, Luca 1 Gabetta, Ester 1 Geymonat, Giuseppe 1 Gramani, L. 1 Graziano, L. 1 Guerri, Luciano 1 Gustafsson, Tony 1 Illner, Reinhard 1 Kawashima, Shuichi 1 Kim, Jeongho 1 Lancellotta, Renato 1 Larosa, Salvatore 1 Latrach, Khalid 1 Le Tallec, Patrick 1 Li, Natasha K. 1 Lods, Bertrand 1 Lowengrub, John Samuel 1 Lumenta, D. B. 1 Málek, Jiří 1 Manzini, Gianmarco 1 Marasco, Addolorata ...and 30 more Co-Authors
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#### Serials

 44 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 23 Mathematical and Computer Modelling 10 Computers & Mathematics with Applications 10 Applied Mathematics Letters 9 Modeling and Simulation in Science, Engineering and Technology 7 L’Aerotecnica, Missili e Spazio 5 Journal of Mathematical Analysis and Applications 5 Series on Advances in Mathematics for Applied Sciences 4 Transport Theory and Statistical Physics 4 Meccanica 3 Mathematics and Computers in Simulation 3 Mechanics Research Communications 3 Discrete and Continuous Dynamical Systems. Series B 3 Networks and Heterogeneous Media 3 Kinetic and Related Models 2 International Journal of Non-Linear Mechanics 2 Journal of Mathematical Physics 2 Reviews in Mathematical Physics 2 Applied Mathematical Modelling 2 Atti della Accademia Nazionale dei Lincei. Serie Ottava. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali 2 Atti della Accademia delle Scienze di Torino. Classe di Scienze Fisiche, Matematiche e Naturali 2 Comptes Rendus de l’Académie des Sciences. Série I 2 Computers and Mathematics with Applications. Part A 2 Journal of Theoretical Medicine 2 Comptes Rendus. Mécanique. Académie des Sciences, Paris 1 International Journal of Modern Physics B 1 Computers and Fluids 1 Journal of Statistical Physics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Atti della Accademia Peloritana dei Pericolanti. Classe di Scienze Fisiche, Matemàtiche e Naturali 1 Journal of Differential Equations 1 Ricerche di Matematica 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Mathematical Modelling 1 Atti del Seminario Matematico e Fisico dell’Università di Modena 1 Communications in Partial Differential Equations 1 SIAM Journal on Applied Mathematics 1 SIAM Review 1 European Mathematical Society Newsletter 1 Mathematics and Mechanics of Solids 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Vietnam Journal of Mathematics 1 Bollettino della Unione Matematica Italiana. Serie VIII. Sezione A. La Matematica nella Società e nella Cultura 1 Nonlinear Analysis. Real World Applications 1 Multiscale Modeling & Simulation 1 Communications in Mathematical Sciences 1 Differential Equations & Nonlinear Mechanics 1 Supplemento ai Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Journal of Physics A: Mathematical and Theoretical 1 Nonlinear Analysis. Hybrid Systems 1 Discrete and Continuous Dynamical Systems. Series S 1 Synthesis Lectures on Mathematics and Statistics 1 S$$\vec{\text{e}}$$MA Journal 1 Journal of Theoretical Biology 1 L’Aerotecnica 1 Transactions of the American Mathematical Society. Series B 1 SpringerBriefs in Mathematics
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#### Fields

 84 Biology and other natural sciences (92-XX) 64 Statistical mechanics, structure of matter (82-XX) 60 Partial differential equations (35-XX) 56 Fluid mechanics (76-XX) 31 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 27 General and overarching topics; collections (00-XX) 24 Probability theory and stochastic processes (60-XX) 18 Operations research, mathematical programming (90-XX) 15 Numerical analysis (65-XX) 14 Integral equations (45-XX) 11 Systems theory; control (93-XX) 8 Ordinary differential equations (34-XX) 8 Dynamical systems and ergodic theory (37-XX) 8 Mechanics of deformable solids (74-XX) 7 Mechanics of particles and systems (70-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Computer science (68-XX) 2 History and biography (01-XX) 2 Operator theory (47-XX) 2 Geophysics (86-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mathematics education (97-XX)

#### Citations contained in zbMATH Open

185 Publications have been cited 3,322 times in 1,605 Documents Cited by Year
Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues. Zbl 1326.35397
Bellomo, N.; Bellouquid, A.; Tao, Y.; Winkler, M.
2015
On the foundations of cancer modelling: selected topics, speculations, and perspectives. Zbl 1151.92014
Bellomo, N.; Li, N. K.; Maini, P. K.
2008
On the modeling of traffic and crowds: a survey of models, speculations, and perspectives. Zbl 1231.90123
Bellomo, Nicola; Dogbe, Christian
2011
Multiscale biological tissue models and flux-limited chemotaxis for multicellular growing systems. Zbl 1402.92065
Bellomo, Nicola; Bellouquid, Abdelghani; Nieto, Juan; Soler, Juan
2010
A survey of models for tumor-immune system dynamics. Zbl 0874.92020
Adam, John A. (ed.); Bellomo, Nicola (ed.)
1997
Modelling and mathematical problems related to tumor evolution and its interaction with the immune system. Zbl 0997.92020
Bellomo, N.; Preziosi, L.
2000
Mathematical topics on the modelling complex multicellular systems and tumor immune cells competition. Zbl 1060.92029
Bellomo, N.; Bellouquid, A.; Delitala, M.
2004
On the difficult interplay between life, “complexity”, and mathematical sciences. Zbl 1315.35137
Bellomo, N.; Knopoff, D.; Soler, J.
2013
On the mathematical theory of the dynamics of swarms viewed as complex systems. Zbl 1242.92065
Bellomo, N.; Soler, J.
2012
Generalized kinetic (Boltzmann) models: mathematical structures and applications. Zbl 1174.82325
Arlotti, L.; Bellomo, N.; De Angelis, E.
2002
Multicellular biological growing systems: hyperbolic limits towards macroscopic description. Zbl 1135.92009
Bellomo, N.; Bellouquid, A.; Nieto, J.; Soler, J.
2007
Modeling complex living systems. A kinetic theory and stochastic game approach. Zbl 1140.91007
Bellomo, Nicola
2008
Modelling mathematical methods and scientific computation. Zbl 0871.65001
Bellomo, Nicola; Preziosi, Luigi
1995
On the modelling crowd dynamics from scaling to hyperbolic macroscopic models. Zbl 1198.92036
Bellomo, Nicola; Dogbé, Christian
2008
Dynamics of tumor interaction with the host immune system. Zbl 0811.92014
Bellomo, N.; Forni, G.
1994
On the Cauchy problem for the nonlinear Boltzmann equation global existence uniqueness and asymptotic stability. Zbl 0561.35074
Bellomo, N.; Toscani, G.
1985
On the mathematical theory of vehicular traffic flow. I: Fluid dynamic and kinetic modelling. Zbl 1041.76061
Bellomo, N.; Delitala, M.; Coscia, V.
2002
Mathematical topics in nonlinear kinetic theory. Zbl 0702.76005
Bellomo, Nicola; Palczewski, Andrzej; Toscani, Giuseppe
1988
On the asymptotic theory from microscopic to macroscopic growing tissue models: an overview with perspectives. Zbl 1328.92023
Bellomo, N.; Bellouquid, A.; Nieto, J.; Soler, J.
2012
Modeling crowd dynamics from a complex system viewpoint. Zbl 1252.35192
Bellomo, Nicola; Piccoli, Benedetto; Tosin, Andrea
2012
Strategies of applied mathematics towards an immuno-mathematical theory on tumors and immune system interactions. Zbl 0947.92014
Bellomo, N.; De Angelis, E.
1998
Nonlinear stochastic systems in physics and mechanics. Zbl 0623.60084
Bellomo, Nicola; Riganti, Riccardo
1987
A comparison between Adomian’s decomposition methods and perturbation techniques for nonlinear random differential equations. Zbl 0575.60064
Bellomo, Nicola; Monaco, Roberto
1985
Nonlinear models and problems in applied sciences from differential quadrature to generalized collocation methods. Zbl 0898.65074
Bellomo, N.
1997
On the dynamics of social conflicts: looking for the black swan. Zbl 1276.82028
Bellomo, Nicola; Herrero, Miguel A.; Tosin, Andrea
2013
A degenerate chemotaxis system with flux limitation: maximally extended solutions and absence of gradient blow-up. Zbl 1430.35166
Bellomo, Nicola; Winkler, Michael
2017
Stochastic evolutionary differential games toward a systems theory of behavioral social dynamics. Zbl 1414.91053
Marsan, G. Ajmone; Bellomo, N.; Gibelli, L.
2016
Toward a mathematical theory of behavioral-social dynamics for pedestrian crowds. Zbl 1325.91042
Bellomo, Nicola; Gibelli, Livio
2015
Multiscale modeling and mathematical problems related to tumor evolution and medical therapy. Zbl 1107.92020
Bellomo, Nicola; De Angelis, Elena; Preziosi, Luigi
2003
Vehicular traffic, crowds, and swarms: from kinetic theory and multiscale methods to applications and research perspectives. Zbl 1431.35211
Albi, G.; Bellomo, N.; Fermo, L.; Ha, S.-Y.; Kim, J.; Pareschi, L.; Poyato, D.; Soler, J.
2019
From the microscale to collective crowd dynamics. Zbl 1280.90019
Bellomo, Nicola; Bellouquid, Abdelghani; Knopoff, Damian
2013
A quest toward a mathematical theory of the dynamics of swarms. Zbl 1366.82077
Bellomo, Nicola; Ha, Seung-Yeal
2017
From a multiscale derivation of nonlinear cross-diffusion models to Keller-Segel models in a Navier-Stokes fluid. Zbl 1353.35038
Bellomo, N.; Bellouquid, A.; Chouhad, N.
2016
Looking for new paradigms towards a biological-mathematical theory of complex multicellular systems. Zbl 1093.92002
Bellomo, Nicola; Forni, Guido
2006
Finite-time blow-up in a degenerate chemotaxis system with flux limitation. Zbl 1367.35044
Bellomo, Nicola; Winkler, Michael
2017
On the onset of non-linearity for diffusion models of binary mixtures of biological materials by asymptotic analysis. Zbl 1160.76403
Bellomo, Nicola; Bellouquid, Abdelghani
2006
From a class of kinetic models to the macroscopic equations for multicellular systems in biology. Zbl 1044.92021
Bellomo, N.; Bellouquid, A.
2004
Towards a mathematical theory of complex socio-economical systems by functional subsystems representation. Zbl 1141.82357
Ajmone Marsan, Giulia; Bellomo, Nicola; Egidi, Massimo
2008
Solution of a new class of nonlinear kinetic models of population dynamics. Zbl 0853.35050
Arlotti, L.; Bellomo, N.
1996
On the multiscale modeling of vehicular traffic: from kinetic to hydrodynamics. Zbl 1302.35372
Bellomo, Nicola; Bellouquid, Abdelghani; Nieto, Juanjo; Soler, Juan
2014
Complexity and mathematical tools toward the modelling of multicellular growing systems. Zbl 1190.92001
Bellomo, N.; Bellouquid, A.; Nieto, J.; Soler, J.
2010
From the modelling of driver’s behavior to hydrodynamic models and problems of traffic flow. Zbl 1005.90016
Bellomo, N.; Marasco, A.; Romano, A.
2002
Kinetic equations modelling population dynamics. Zbl 0946.92019
Arlotti, L.; Bellomo, N.; Lachowicz, M.
2000
From the Jager and Segel model to kinetic population dynamics nonlinear evolution problems and applications. Zbl 1043.92518
Arlotti, L.; Bellomo, N.; Latrach, K.
1999
Bifurcation analysis for a nonlinear system of integro-differential equations modelling tumor-immune cells competition. Zbl 0932.92016
Bellomo, N.; Firmani, B.; Guerri, L.
1999
Stochastic partial differential equations in continuum physics - on the foundations of the stochastic interpolation method for Ito’s type equations. Zbl 0706.60063
Bellomo, N.; Flandoli, F.
1989
Mathematical topics in nonlinear kinetic theory II. The Enskog equation. Zbl 0733.76061
Bellomo, N.; Lachowicz, M.; Polewczak, J.; Toscani, G.
1991
Solution of nonlinear initial-boundary value problems by sinc collocation-interpolation methods. Zbl 0822.65075
Bellomo, N.; Ridolfi, L.
1995
On multiscale models of Pedestrian crowds from mesoscopic to macroscopic. Zbl 1329.90029
Bellomo, Nicola; Bellouquid, Abdelghani
2015
Solution of nonlinear problems in applied sciences by generalized collocation methods and Mathematica. Zbl 1058.65110
Bellomo, N.; De Angelis, E.; Graziano, L.; Romano, A.
2001
Population dynamics with stochastic interaction. Zbl 0838.92018
Arlotti, L.; Bellomo, N.
1995
On Adomian’s decomposition method and some comparisons with Picard’s iterative scheme. Zbl 0624.60079
Bellomo, N.; Sarafyan, D.
1987
First-order models and closure of the mass conservation equation in the mathematical theory of vehicular traffic flow. Zbl 1177.90076
Bellomo, Nicola; Coscia, Vincenzo
2005
The modelling of the immune competition by generalized kinetic (Boltzmann) models: Review and research perspectives. Zbl 1022.92012
Bellomo, N.; Bellouquid, A.; De Angelis, E.
2003
On the modeling of crowd dynamics: looking at the beautiful shapes of swarms. Zbl 1260.90052
Bellomo, Nicola; Bellouquid, Abdelghani
2011
Crowd dynamics on a moving platform: mathematical modelling and application to lively footbridges. Zbl 1198.74031
Venuti, Fiammetta; Bruno, Luca; Bellomo, Nicola
2007
Mathematics and complexity in life and human sciences. Zbl 1218.92001
Bellomo, N.; Berestycki, H.; Brezzi, F.; Nadal, J.-P.
2010
Lecture notes on the mathematical theory of generalized Boltzmann models. Zbl 0983.82012
Bellomo, Nicola; Lo Schiavo, Mauro
2000
On the initial value problem for the Boltzmann equation with a force term. Zbl 0699.35237
Bellomo, N.; Lachowicz, M.; Palczewski, A.; Toscani, G.
1989
From a systems theory of sociology to modeling the onset and evolution of criminality. Zbl 1403.91278
Bellomo, Nicola; Colasuonno, Francesca; Knopoff, Damián; Soler, Juan
2015
From microscopic to macroscopic description of multicellular systems and biological growing tissues. Zbl 1121.92025
Bellomo, Nicola; Bellouquid, Abdelghani; Herrero, Miguel A.
2007
Modeling in applied sciences. A kinetic theory approach. Zbl 0938.00011
Bellomo, Nicola (ed.); Pulvirenti, Mario (ed.)
2000
From the Boltzmann equation to generalized kinetic models in applied sciences. Zbl 0897.76082
Bellomo, N.; Lo Schiavo, M.
1997
Traffic, crowds, and swarms. Zbl 1171.90361
Bellomo, N.; Brezzi, F.
2008
On the interplay between behavioral dynamics and social interactions in human crowds. Zbl 1420.91384
Bellomo, Nicola; Gibelli, Livio; Outada, Nisrine
2019
Complex systems and society. Modeling and simulation. Zbl 1328.00108
Ajmone Marsan, Giulia; Bellomo, Nicola; Tosin, Andrea
2013
On a class of integro-differential equations modeling complex systems with nonlinear interactions. Zbl 1243.82046
Arlotti, L.; De Angelis, E.; Fermo, L.; Lachowicz, M.; Bellomo, N.
2012
The Enskog-Boltzmann equation in the whole space $${\mathbb{R}}^ 3:$$ Some global existence, uniqueness and stability results. Zbl 0633.35072
Toscani, G.; Bellomo, N.
1987
Active particles, Volume 1. Advances in theory, models, and applications. Zbl 1368.00045
Bellomo, Nicola (ed.); Degond, Pierre (ed.); Tadmor, Eitan (ed.)
2017
Behavioral crowds: modeling and Monte Carlo simulations toward validation. Zbl 1390.65030
Bellomo, N.; Gibelli, L.
2016
Nonlinear stochastic evolution problems in applied sciences. Zbl 0770.60061
Bellomo, N.; Brzezniak, Z.; de Socio, L. M.
1992
The discrete Boltzmann equation: A review of the mathematical aspects of the initial and initial-boundary value problems. Zbl 0737.76065
Bellomo, N.; Gustafsson, T.
1991
Modeling the hiding-learning dynamics in large living systems. Zbl 1198.37117
Bellomo, N.
2010
Selected topics in cancer modeling. Genesis, evolution, immune competition, and therapy. Zbl 1149.92015
Bellomo, Nicola (ed.); Chaplain, Mark (ed.); De Angelis, Elena (ed.)
2008
The discrete Boltzmann equation with multiple collisions: Global existence and stability for the initial value problem. Zbl 0706.76084
Bellomo, N.; Kawashima, S.
1990
Occurrence vs. absence of taxis-driven instabilities in a May-Nowak model for virus infection. Zbl 1428.35615
Bellomo, Nicola; Painter, Kevin J.; Tao, Youshan; Winkler, Michael
2019
A quest towards a mathematical theory of living systems. Zbl 1381.92001
Bellomo, Nicola; Bellouquid, Abdelghani; Gibelli, Livio; Outada, Nisrine
2017
Modeling behavioral social systems. Zbl 1355.00017
Bellomo, N. (ed.); Brezzi, F. (ed.); Pulvirenti, M. (ed.)
2017
On the mathematical theory of living systems. II: The interplay between mathematics and system biology. Zbl 1236.92005
Coscia, V.; Fermo, L.; Bellomo, N.
2011
Preface: Challenging mathematical problems in cancer modelling. Zbl 1210.00049
Bellomo, N.; Maini, P. K.
2007
Modelling tumor progression, heterogeneity, and immune competition. Zbl 1050.92026
Ambrosi, D.; Bellomo, N.; Preziosi, L.
2002
Time evolution and fluctuations of the probability density and entropy function for a class of nonlinear stochastic systems in mathematical physics. Zbl 0604.93052
Bellomo, N.; Riganti, R.
1986
Mathematics, complexity and multiscale features of large systems of self-propelled particles. Zbl 1398.92024
Bellomo, N.; Brezzi, F.
2016
Mathematics and complexity in human and life sciences. Zbl 1175.00022
Bellomo, N.; Berestycki, H.; Brezzi, F.; Nadal, J.-P.
2009
Generalized kinetic models in applied sciences. Lecture notes on mathematical problem. Zbl 1073.82001
Arlotti, Luisa; Bellomo, Nicola; De Angelis, Elena; Lachowicz, Miroslaw
2003
Nonlinear kinetic equations with dissipative collisions. Zbl 0835.76091
Bellomo, Nicola; Esteban, Maria Jesus; Lachowicz, Mirosław
1995
The semicontinuous Boltzmann equation: Towards a model for fluid dynamic applications. Zbl 0770.76057
Longo, E.; Preziosi, L.; Bellomo, N.
1993
Random heat equation: Solutions by the stochastic adaptive interpolation method. Zbl 0661.60082
Bellomo, N.; de Socio, L. M.; Monaco, R.
1988
Time-evolution of the probability density under the action of a deterministic dynamical system. Zbl 0475.70019
Bellomo, N.; Pistone, G.
1980
Stabilization in a chemotaxis model for virus infection. Zbl 1439.35052
Bellomo, Nicola; Tao, Youshan
2020
Modeling chemotaxis from $$L^2$$-closure moments in kinetic theory of active particles. Zbl 1280.35160
Bellomo, Nicola; Bellouquid, Abdelghani; Nieto, Juanjo; Soler, Juan
2013
Mathematics and complexity of multi-particle systems. Zbl 1242.92003
Bellomo, N.; Brezzi, F.
2012
On the derivation of macroscopic tissue equations from hybrid models of the kinetic theory of multicellular growing systems – the effect of global equilibrium. Zbl 1184.93071
Bellomo, N.; Bellouquid, A.
2009
Mathematical tools of the kinetic theory of active particles with some reasoning on the modelling progression and heterogeneity. Zbl 1165.82319
De Lillo, S.; Salvatori, M. C.; Bellomo, N.
2007
Mechanics and dynamical systems with $$Mathematica$$. Zbl 0962.70006
Bellomo, Nicola; Preziosi, Luigi; Romano, Antonio
2000
Lecture Notes on the mathematical theory of the Boltzmann equation. Zbl 0871.76074
Bellomo, N. (ed.)
1995
On the asymptotic equivalence between the Enskog and the Boltzmann equations. Zbl 1086.82539
Bellomo, N.; Lachowicz, M.
1988
On the mathematical modelling of physical systems by ordinary differential stochastic equations. Zbl 0547.60060
Bellomo, N.; Cafaro, E.; Rizzi, G.
1984
Mathematics and complexity in biological sciences. Zbl 1328.00110
Bellomo, N.; Brezzi, F.
2011
Generalized collocation methods. Solutions to nonlinear problems. Zbl 1135.65038
Bellomo, Nicola; Lods, Bertrand; Revelli, Roberto; Ridolfi, Luca
2008
Stabilization in a chemotaxis model for virus infection. Zbl 1439.35052
Bellomo, Nicola; Tao, Youshan
2020
A unified multiscale vision of behavioral crowds. Zbl 1434.91046
Aylaj, Bouchra; Bellomo, Nicola; Gibelli, Livio; Reali, Alessandro
2020
Active particles methods and challenges in behavioral systems. Zbl 1454.35392
Bellomo, N.; Brezzi, F.; Soler, J.
2020
A multiscale model of virus pandemic: heterogeneous interactive entities in a globally connected world. Zbl 1451.92276
Bellomo, Nicola; Bingham, Richard; Chaplain, Mark A. J.; Dosi, Giovanni; Forni, Guido; Knopoff, Damian A.; Lowengrub, John; Twarock, Reidun; Virgillito, Maria Enrica
2020
From particles to firms: on the kinetic theory of climbing up evolutionary landscapes. Zbl 1445.82020
Bellomo, Nicola; Dosi, Giovanni; Knopoff, Damián A.; Virgillito, Maria Enrica
2020
Vehicular traffic, crowds, and swarms: from kinetic theory and multiscale methods to applications and research perspectives. Zbl 1431.35211
Albi, G.; Bellomo, N.; Fermo, L.; Ha, S.-Y.; Kim, J.; Pareschi, L.; Poyato, D.; Soler, J.
2019
On the interplay between behavioral dynamics and social interactions in human crowds. Zbl 1420.91384
Bellomo, Nicola; Gibelli, Livio; Outada, Nisrine
2019
Occurrence vs. absence of taxis-driven instabilities in a May-Nowak model for virus infection. Zbl 1428.35615
Bellomo, Nicola; Painter, Kevin J.; Tao, Youshan; Winkler, Michael
2019
Active particles, Volume 2. Advances in theory, models, and applications. Zbl 1427.74004
Bellomo, Nicola (ed.); Degond, Pierre (ed.); Tadmor, Eitan (ed.)
2019
Challenges in active particles methods: theory and applications. Zbl 1411.35149
Bellomo, N.; Brezzi, F.
2018
Cross-diffusion models: analytic and multiscale problems. Zbl 1408.35078
Bellomo, N.; Tao, Y.; Winkler, M.
2018
Crowd dynamics, Volume 1. Theory, models, and safety problems. Zbl 1410.92004
Gibelli, Livio (ed.); Bellomo, Nicola (ed.)
2018
A degenerate chemotaxis system with flux limitation: maximally extended solutions and absence of gradient blow-up. Zbl 1430.35166
Bellomo, Nicola; Winkler, Michael
2017
A quest toward a mathematical theory of the dynamics of swarms. Zbl 1366.82077
Bellomo, Nicola; Ha, Seung-Yeal
2017
Finite-time blow-up in a degenerate chemotaxis system with flux limitation. Zbl 1367.35044
Bellomo, Nicola; Winkler, Michael
2017
Active particles, Volume 1. Advances in theory, models, and applications. Zbl 1368.00045
Bellomo, Nicola (ed.); Degond, Pierre (ed.); Tadmor, Eitan (ed.)
2017
A quest towards a mathematical theory of living systems. Zbl 1381.92001
Bellomo, Nicola; Bellouquid, Abdelghani; Gibelli, Livio; Outada, Nisrine
2017
Modeling behavioral social systems. Zbl 1355.00017
Bellomo, N. (ed.); Brezzi, F. (ed.); Pulvirenti, M. (ed.)
2017
Mathematical models of self-propelled particles. Zbl 1370.82034
Bellomo, N.; Brezzi, F.
2017
Stochastic evolutionary differential games toward a systems theory of behavioral social dynamics. Zbl 1414.91053
Marsan, G. Ajmone; Bellomo, N.; Gibelli, L.
2016
From a multiscale derivation of nonlinear cross-diffusion models to Keller-Segel models in a Navier-Stokes fluid. Zbl 1353.35038
Bellomo, N.; Bellouquid, A.; Chouhad, N.
2016
Behavioral crowds: modeling and Monte Carlo simulations toward validation. Zbl 1390.65030
Bellomo, N.; Gibelli, L.
2016
Mathematics, complexity and multiscale features of large systems of self-propelled particles. Zbl 1398.92024
Bellomo, N.; Brezzi, F.
2016
Macroscopic first order models of multicomponent human crowds with behavioral dynamics. Zbl 1356.91079
Bellomo, N.; Berrone, S.; Gibelli, L.; Pieri, A. B.
2016
Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues. Zbl 1326.35397
Bellomo, N.; Bellouquid, A.; Tao, Y.; Winkler, M.
2015
Toward a mathematical theory of behavioral-social dynamics for pedestrian crowds. Zbl 1325.91042
Bellomo, Nicola; Gibelli, Livio
2015
On multiscale models of Pedestrian crowds from mesoscopic to macroscopic. Zbl 1329.90029
Bellomo, Nicola; Bellouquid, Abdelghani
2015
From a systems theory of sociology to modeling the onset and evolution of criminality. Zbl 1403.91278
Bellomo, Nicola; Colasuonno, Francesca; Knopoff, Damián; Soler, Juan
2015
Traffic, crowds, and dynamics of self-organized particles: new trends and challenges. Zbl 1308.92110
Bellomo, Nicola; Brezzi, Franco
2015
On the derivation of angiogenesis tissue models: from the micro-scale to the macro-scale. Zbl 1327.76175
Bellomo, Nicola; Bellouquid, Abdelghani
2015
On the multiscale modeling of vehicular traffic: from kinetic to hydrodynamics. Zbl 1302.35372
Bellomo, Nicola; Bellouquid, Abdelghani; Nieto, Juanjo; Soler, Juan
2014
Recent techniques for PDE discretizations on polyhedral meshes. Zbl 1291.65317
Bellomo, N.; Brezzi, F.; Manzini, G.
2014
Complex systems: new challenges with modeling headaches. Zbl 1280.00033
Bellomo, N.; Brezzi, Franco
2014
On the difficult interplay between life, “complexity”, and mathematical sciences. Zbl 1315.35137
Bellomo, N.; Knopoff, D.; Soler, J.
2013
On the dynamics of social conflicts: looking for the black swan. Zbl 1276.82028
Bellomo, Nicola; Herrero, Miguel A.; Tosin, Andrea
2013
From the microscale to collective crowd dynamics. Zbl 1280.90019
Bellomo, Nicola; Bellouquid, Abdelghani; Knopoff, Damian
2013
Complex systems and society. Modeling and simulation. Zbl 1328.00108
Ajmone Marsan, Giulia; Bellomo, Nicola; Tosin, Andrea
2013
Modeling chemotaxis from $$L^2$$-closure moments in kinetic theory of active particles. Zbl 1280.35160
Bellomo, Nicola; Bellouquid, Abdelghani; Nieto, Juanjo; Soler, Juan
2013
Sources of nonlinearity in the kinetic theory for active particles with focus on the formation of political opinions. Zbl 1315.91054
Bellomo, Nicola; Coscia, Vincenzo
2013
Heterogeneous distribution of mechanical stress in human lung: a mathematical approach to evaluate abnormal remodeling in IPF. Zbl 1330.92019
Carloni, A.; Poletti, V.; Fermo, L.; Bellomo, N.; Chilosi, M.
2013
On the mathematical theory of the dynamics of swarms viewed as complex systems. Zbl 1242.92065
Bellomo, N.; Soler, J.
2012
On the asymptotic theory from microscopic to macroscopic growing tissue models: an overview with perspectives. Zbl 1328.92023
Bellomo, N.; Bellouquid, A.; Nieto, J.; Soler, J.
2012
Modeling crowd dynamics from a complex system viewpoint. Zbl 1252.35192
Bellomo, Nicola; Piccoli, Benedetto; Tosin, Andrea
2012
On a class of integro-differential equations modeling complex systems with nonlinear interactions. Zbl 1243.82046
Arlotti, L.; De Angelis, E.; Fermo, L.; Lachowicz, M.; Bellomo, N.
2012
Mathematics and complexity of multi-particle systems. Zbl 1242.92003
Bellomo, N.; Brezzi, F.
2012
Global solution to the Cauchy problem for discrete velocity models of vehicular traffic. Zbl 1230.35056
Bellomo, N.; Bellouquid, A.
2012
On the modeling of traffic and crowds: a survey of models, speculations, and perspectives. Zbl 1231.90123
Bellomo, Nicola; Dogbe, Christian
2011
On the modeling of crowd dynamics: looking at the beautiful shapes of swarms. Zbl 1260.90052
Bellomo, Nicola; Bellouquid, Abdelghani
2011
On the mathematical theory of living systems. II: The interplay between mathematics and system biology. Zbl 1236.92005
Coscia, V.; Fermo, L.; Bellomo, N.
2011
Mathematics and complexity in biological sciences. Zbl 1328.00110
Bellomo, N.; Brezzi, F.
2011
Towards a mathematical theory of complex biological systems. Zbl 1286.92003
Bianca, Carlo; Bellomo, Nicola
2011
On the modeling of crowd dynamics: an overview and research perspectives. Zbl 1242.90053
Bellomo, Nicola; Bianca, Carlo; Coscia, Vincenzo
2011
On the modeling of collective learning dynamics. Zbl 1233.92002
De Lillo, S.; Bellomo, N.
2011
Continuum thermodynamics and nonlinear partial differential equations. Zbl 1213.80002
Bellomo, N.; Málek, J.
2011
Multiscale biological tissue models and flux-limited chemotaxis for multicellular growing systems. Zbl 1402.92065
Bellomo, Nicola; Bellouquid, Abdelghani; Nieto, Juan; Soler, Juan
2010
Complexity and mathematical tools toward the modelling of multicellular growing systems. Zbl 1190.92001
Bellomo, N.; Bellouquid, A.; Nieto, J.; Soler, J.
2010
Mathematics and complexity in life and human sciences. Zbl 1218.92001
Bellomo, N.; Berestycki, H.; Brezzi, F.; Nadal, J.-P.
2010
Modeling the hiding-learning dynamics in large living systems. Zbl 1198.37117
Bellomo, N.
2010
On the modeling of nonlinear interactions in large complex systems. Zbl 1197.92002
Bellomo, N.; Bianca, C.; Mongiovì, M. S.
2010
On the modelling of vehicular traffic and crowds by kinetic theory of active particles. Zbl 1211.91210
Bellomo, Nicola; Bellouquid, Abdelghani
2010
Mathematics and complexity in human and life sciences. Zbl 1175.00022
Bellomo, N.; Berestycki, H.; Brezzi, F.; Nadal, J.-P.
2009
On the derivation of macroscopic tissue equations from hybrid models of the kinetic theory of multicellular growing systems – the effect of global equilibrium. Zbl 1184.93071
Bellomo, N.; Bellouquid, A.
2009
On the coupling of higher and lower scales using the mathematical kinetic theory of active particles. Zbl 1162.92013
Bellomo, N.; Delitala, M.
2009
From the mathematical kinetic theory for active particles on the derivation of hyperbolic macroscopic tissue models. Zbl 1171.92309
Bellomo, Nicola; Bellouquid, Abdelghani; Soler, Juan
2009
On the derivation of macroscopic hyperbolic equations for binary multicellular growing mixtures. Zbl 1186.35131
Bellomo, N.; Bellouquid, A.
2009
On the foundations of cancer modelling: selected topics, speculations, and perspectives. Zbl 1151.92014
Bellomo, N.; Li, N. K.; Maini, P. K.
2008
Modeling complex living systems. A kinetic theory and stochastic game approach. Zbl 1140.91007
Bellomo, Nicola
2008
On the modelling crowd dynamics from scaling to hyperbolic macroscopic models. Zbl 1198.92036
Bellomo, Nicola; Dogbé, Christian
2008
Towards a mathematical theory of complex socio-economical systems by functional subsystems representation. Zbl 1141.82357
Ajmone Marsan, Giulia; Bellomo, Nicola; Egidi, Massimo
2008
Traffic, crowds, and swarms. Zbl 1171.90361
Bellomo, N.; Brezzi, F.
2008
Selected topics in cancer modeling. Genesis, evolution, immune competition, and therapy. Zbl 1149.92015
Bellomo, Nicola (ed.); Chaplain, Mark (ed.); De Angelis, Elena (ed.)
2008
Generalized collocation methods. Solutions to nonlinear problems. Zbl 1135.65038
Bellomo, Nicola; Lods, Bertrand; Revelli, Roberto; Ridolfi, Luca
2008
On the complexity of multiple interactions with additional reasonings about Kate, Jules and Jim. Zbl 1144.82339
Bellomo, Nicola; Carbonaro, Bruno
2008
From the mathematical kinetic theory of active particles to multiscale modelling of complex biological systems. Zbl 1134.92003
Bellomo, N.; Bellouquid, A.; Delitala, M.
2008
On the kinetic and stochastic games theory for active particles: Some reasonings on open large living systems. Zbl 1187.91159
Bellomo, N.; Carbonaro, B.; Gramani, L.
2008
Multicellular biological growing systems: hyperbolic limits towards macroscopic description. Zbl 1135.92009
Bellomo, N.; Bellouquid, A.; Nieto, J.; Soler, J.
2007
Crowd dynamics on a moving platform: mathematical modelling and application to lively footbridges. Zbl 1198.74031
Venuti, Fiammetta; Bruno, Luca; Bellomo, Nicola
2007
From microscopic to macroscopic description of multicellular systems and biological growing tissues. Zbl 1121.92025
Bellomo, Nicola; Bellouquid, Abdelghani; Herrero, Miguel A.
2007
Preface: Challenging mathematical problems in cancer modelling. Zbl 1210.00049
Bellomo, N.; Maini, P. K.
2007
Mathematical tools of the kinetic theory of active particles with some reasoning on the modelling progression and heterogeneity. Zbl 1165.82319
De Lillo, S.; Salvatori, M. C.; Bellomo, N.
2007
Looking for new paradigms towards a biological-mathematical theory of complex multicellular systems. Zbl 1093.92002
Bellomo, Nicola; Forni, Guido
2006
On the onset of non-linearity for diffusion models of binary mixtures of biological materials by asymptotic analysis. Zbl 1160.76403
Bellomo, Nicola; Bellouquid, Abdelghani
2006
On the modelling of complex sociopsychological systems with some reasoning about Kate, Jules, and Jim. Zbl 1200.91258
Bellomo, Nicola; Carbonaro, Bruno
2006
On the mathematical kinetic theory of active particles with discrete states: The derivation of macroscopic equations. Zbl 1130.92006
Bellomo, Nicola; Bellouquid, Abdelghani
2006
First-order models and closure of the mass conservation equation in the mathematical theory of vehicular traffic flow. Zbl 1177.90076
Bellomo, Nicola; Coscia, Vincenzo
2005
Mathematical topics on the modelling complex multicellular systems and tumor immune cells competition. Zbl 1060.92029
Bellomo, N.; Bellouquid, A.; Delitala, M.
2004
From a class of kinetic models to the macroscopic equations for multicellular systems in biology. Zbl 1044.92021
Bellomo, N.; Bellouquid, A.
2004
From the mathematical kinetic theory to modelling complex systems in applied sciences. Zbl 1073.82034
Bellomo, Nicola
2004
Multiscale modeling and mathematical problems related to tumor evolution and medical therapy. Zbl 1107.92020
Bellomo, Nicola; De Angelis, Elena; Preziosi, Luigi
2003
The modelling of the immune competition by generalized kinetic (Boltzmann) models: Review and research perspectives. Zbl 1022.92012
Bellomo, N.; Bellouquid, A.; De Angelis, E.
2003
Generalized kinetic models in applied sciences. Lecture notes on mathematical problem. Zbl 1073.82001
Arlotti, Luisa; Bellomo, Nicola; De Angelis, Elena; Lachowicz, Miroslaw
2003
Non-linear consolidation models of clay which change type. Zbl 1346.74131
Battaglio, M.; Bellomo, N.; Bonzani, I.; Lancellotta, R.
2003
The generalized kinetic modelling of a multicomponent “real-life” fluid by means of a single distribution function. Zbl 1106.76326
Bellomo, N.; Mamontov, E.; Willander, M.
2003
Lectures notes on the discretization of the Boltzmann equation. Zbl 1118.82041
Bellomo, Nicola (ed.); Gatignol, Renée (ed.)
2003
Cancer immune system competition: modelling and bifurcation problems. Zbl 1337.92098
Bellomo, Nicola; Bertotti, Maria Letizia; Motta, Santo
2003
The generalized-kinetics-based equilibrium distribution function for composite particles. Zbl 1177.82058
Bellomo, Nicola; Calander, Nils; Mamontov, Eugen; Willander, Magnus
2003
Boundary value steady solutions of a class of hydrodynamic models for vehicular traffic flow. Zbl 1080.90017
Bertotti, M. L.; Bellomo, N.
2003
Generalized kinetic (Boltzmann) models: mathematical structures and applications. Zbl 1174.82325
Arlotti, L.; Bellomo, N.; De Angelis, E.
2002
On the mathematical theory of vehicular traffic flow. I: Fluid dynamic and kinetic modelling. Zbl 1041.76061
Bellomo, N.; Delitala, M.; Coscia, V.
2002
From the modelling of driver’s behavior to hydrodynamic models and problems of traffic flow. Zbl 1005.90016
Bellomo, N.; Marasco, A.; Romano, A.
2002
...and 85 more Documents
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#### Cited by 1,928 Authors

 113 Bellomo, Nicola 48 Ha, Seung-Yeal 44 Winkler, Michael 32 Lachowicz, Mirosław 29 Tao, Youshan 27 Bellouquid, Abdelghani 26 Delitala, Marcello 24 Bonzani, Ida 19 De Angelis, Elena 19 Zheng, Jiashan 18 Soler, Juan S. 18 Toscani, Giuseppe 17 Mu, Chunlai 16 Bianca, Carlo 16 Piccoli, Benedetto 15 Degond, Pierre 15 Surulescu, Christina 14 Brezzi, Franco 14 Knopoff, Damian A. 14 Lankeit, Johannes 13 Klar, Axel 13 Monaco, Roberto 13 Perthame, Benoît 13 Preziosi, Luigi 13 Shen, Wenxian 12 Xiang, Tian 11 Chaplain, Mark A. J. 11 Herty, Michael Matthias 11 Mizukami, Masaaki 11 Wang, Zhian 11 Xiang, Zhaoyin 10 Bertotti, Maria Letizia 10 Black, Tobias 10 Cui, Shangbin 10 Dolfin, Marina 10 Ren, Guoqiang 10 Salako, Rachidi Bolaji 10 Wang, Liangchen 10 Yokota, Tomomi 9 Adomian, George 9 Borsche, Raul 9 Cattani, Carlo 9 Coscia, Vincenzo 9 Eftimie, Raluca 9 Jin, Hai-Yang 9 Kolev, Mikhail K. 9 Lin, Ke 9 Lo Schiavo, Mauro 9 Mamontov, E. V. 9 Tosin, Andrea 8 Arlotti, Luisa 8 Dogbé, Christian 8 d’Onofrio, Alberto 8 Fermo, Luisa 8 Fujie, Kentarou 8 Gibelli, Livio 8 Kim, Doheon 8 Nieto, Juanjo 8 Oden, John Tinsley 8 Pareschi, Lorenzo 8 Riganti, Riccardo 8 Viglialoro, Giuseppe 8 Wang, Yifu 8 Wang, Yulan 8 Zhang, Xianwen 7 Carbonaro, Bruno 7 Carrillo de la Plata, José Antonio 7 D’Acunto, Berardino 7 Duan, Junsheng 7 Duan, Renjun 7 Elaiw, Ahmed M. 7 Guo, Qian 7 Herrero, Miguel Ángel 7 Jiang, Jie 7 Kim, Jeongho 7 Lowengrub, John Samuel 7 Mussone, Lorenzo 7 Park, Hansol 7 Ridolfi, Luca 7 Straughan, Brian 7 Yun, Seok-Bae 7 Zubik-Kowal, Barbara 6 Bae, Hyeong-Ohk 6 Bertozzi, Andrea Louise 6 Cao, Xinru 6 Dimarco, Giacomo 6 Dong, Jiu-Gang 6 Göttlich, Simone 6 Kim, Dohyun 6 Komarova, Natalia L. 6 Liu, Gui-Rong 6 Liu, Zuhan 6 López, Álvaro G. 6 Polewczak, Jacek 6 Sanjuán, Miguel A. F. 6 Seoane, Jesús M. 6 Stinner, Christian 6 Tello, José Ignacio 6 Wazwaz, Abdul-Majid Abdul-Rahman 6 Wei, Jinbo ...and 1,828 more Authors
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#### Cited in 222 Serials

 269 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 140 Mathematical and Computer Modelling 76 Journal of Differential Equations 71 Computers & Mathematics with Applications 66 Journal of Mathematical Analysis and Applications 44 Applied Mathematics and Computation 43 Applied Mathematics Letters 38 Nonlinear Analysis. Real World Applications 36 Journal of Theoretical Biology 33 Journal of Statistical Physics 29 Discrete and Continuous Dynamical Systems. Series B 27 ZAMP. Zeitschrift für angewandte Mathematik und Physik 24 Transport Theory and Statistical Physics 21 Journal of Mathematical Biology 21 Applied Mathematical Modelling 21 Discrete and Continuous Dynamical Systems 19 Bulletin of Mathematical Biology 18 Networks and Heterogeneous Media 17 Journal of Mathematical Physics 16 Mathematical Biosciences 15 Kinetic and Related Models 14 Mathematical Methods in the Applied Sciences 14 SIAM Journal on Applied Mathematics 14 SIAM Journal on Mathematical Analysis 14 Discrete and Continuous Dynamical Systems. Series S 13 Archive for Rational Mechanics and Analysis 12 Journal of Computational and Applied Mathematics 12 Mathematics and Computers in Simulation 11 Nonlinearity 11 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 10 Acta Applicandae Mathematicae 10 International Journal of Biomathematics 9 Journal of Nonlinear Science 9 Mathematical Biosciences and Engineering 8 Physica D 8 Computational & Mathematical Methods in Medicine 7 Journal of Computational Physics 7 Physica A 7 Meccanica 7 Journal of Dynamics and Differential Equations 7 Calculus of Variations and Partial Differential Equations 7 NoDEA. Nonlinear Differential Equations and Applications 7 Abstract and Applied Analysis 7 Communications in Applied and Industrial Mathematics 6 Applicable Analysis 6 SIAM Journal on Control and Optimization 6 Computational and Applied Mathematics 5 Quarterly of Applied Mathematics 5 Communications in Partial Differential Equations 5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 5 Continuum Mechanics and Thermodynamics 5 Communications on Pure and Applied Analysis 4 Computer Methods in Applied Mechanics and Engineering 4 Journal of Engineering Mathematics 4 Chaos, Solitons and Fractals 4 Numerical Methods for Partial Differential Equations 4 Journal of Scientific Computing 4 Japan Journal of Industrial and Applied Mathematics 4 Journal of Mathematical Sciences (New York) 4 Communications in Nonlinear Science and Numerical Simulation 4 Nonlinear Analysis. Hybrid Systems 4 Asian-European Journal of Mathematics 3 Acta Mechanica 3 Computers and Fluids 3 Communications in Mathematical Physics 3 International Journal of Engineering Science 3 International Journal for Numerical Methods in Engineering 3 Kybernetes 3 SIAM Journal on Numerical Analysis 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Mathematical Problems in Engineering 3 Mathematical Population Studies 3 Mathematics and Mechanics of Solids 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Chaos 3 Journal of Biological Systems 3 Archives of Computational Methods in Engineering 3 Journal of Applied Mathematics 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 SIAM Journal on Applied Dynamical Systems 3 Multiscale Modeling & Simulation 3 Mathematical Modelling of Natural Phenomena 2 International Journal of Theoretical Physics 2 Physics Letters. A 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Applied Mathematics and Optimization 2 Funkcialaj Ekvacioj. Serio Internacia 2 Proceedings of the American Mathematical Society 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Rendiconti del Seminario Matematico della Università di Padova 2 Theoretical Population Biology 2 Stochastic Analysis and Applications 2 Applied Numerical Mathematics 2 European Journal of Applied Mathematics 2 Applications of Mathematics 2 International Journal of Computer Mathematics 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Topological Methods in Nonlinear Analysis 2 Applied Mathematics. Series B (English Edition) 2 Discrete Dynamics in Nature and Society ...and 122 more Serials
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#### Cited in 46 Fields

 863 Partial differential equations (35-XX) 861 Biology and other natural sciences (92-XX) 243 Statistical mechanics, structure of matter (82-XX) 230 Numerical analysis (65-XX) 213 Fluid mechanics (76-XX) 158 Ordinary differential equations (34-XX) 143 Operations research, mathematical programming (90-XX) 135 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 111 Probability theory and stochastic processes (60-XX) 81 Integral equations (45-XX) 74 Dynamical systems and ergodic theory (37-XX) 56 Systems theory; control (93-XX) 52 Calculus of variations and optimal control; optimization (49-XX) 51 Mechanics of deformable solids (74-XX) 27 Mechanics of particles and systems (70-XX) 20 Statistics (62-XX) 18 Operator theory (47-XX) 16 Computer science (68-XX) 16 Classical thermodynamics, heat transfer (80-XX) 14 General and overarching topics; collections (00-XX) 9 Optics, electromagnetic theory (78-XX) 8 Information and communication theory, circuits (94-XX) 7 Difference and functional equations (39-XX) 7 Geophysics (86-XX) 6 Combinatorics (05-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Quantum theory (81-XX) 4 Functional analysis (46-XX) 3 Real functions (26-XX) 3 Measure and integration (28-XX) 3 Differential geometry (53-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Topological groups, Lie groups (22-XX) 2 Special functions (33-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Manifolds and cell complexes (57-XX) 2 Mathematics education (97-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 Convex and discrete geometry (52-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX)