Edit Profile (opens in new tab) Toscani, Giuseppe Compute Distance To: Compute Author ID: toscani.giuseppe Published as: Toscani, Giuseppe; Toscani, G. Homepage: http://www-dimat.unipv.it/toscani/ External Links: MGP · ORCID · Google Scholar · ResearchGate · dblp · GND Documents Indexed: 215 Publications since 1975, including 3 Books 9 Contributions as Editor Co-Authors: 95 Co-Authors with 170 Joint Publications 2,299 Co-Co-Authors all top 5 Co-Authors 54 single-authored 23 Pareschi, Lorenzo 19 Carrillo de la Plata, José Antonio 13 Pulvirenti, Ada 11 Naldi, Giovanni 10 Gabetta, Ester 8 Bellomo, Nicola 8 Furioli, Giulia 8 Terraneo, Elide 7 Markowich, Peter Alexander 7 Matthes, Daniel 7 Spiga, Giampiero 7 Zanella, Mattia 6 Bisi, Marzia 6 Comincioli, Valeriano 6 Dolbeault, Jean 6 Jüngel, Ansgar 5 Arnold, Anton 5 Gosse, Laurent 5 Villani, Cédric 4 Brugna, Carlo 4 Dimarco, Giacomo 4 Fornasier, Massimo 4 Gualandi, Stefano 4 Monaco, Roberto 3 Bassetti, Federico 3 Bobylev, Alexandre Vasiljévitch 3 Düring, Bertram 3 Frosali, Giovanni 3 Lods, Bertrand 3 López, José Luis 3 Palczewski, Andrzej 3 Savaré, Giuseppe 3 Soler, Juan S. 3 Unterreiter, Andreas 2 Azzi, Mara 2 Bardelli, Chiara 2 Bertoluzza, Carlo 2 Boffi, Vinicio C. 2 Cáceres, María-José 2 Cordier, Stéphane 2 Deandrea, Silvia 2 Desvillettes, Laurent 2 Di Francesco, Marco 2 Figini, Silvia 2 Gualdani, Maria Pia 2 Jin, Shi 2 Lachowicz, Mirosław 2 Lederman, Claudia B. 2 Lions, Pierre-Louis 2 Perotti, Pietro 2 Protopopescu, Vladimir A. 2 Salvarani, Francesco 2 Torregrossa, Marco 2 Tosin, Andrea 2 Wennberg, Bernt 1 Aletti, Giacomo 1 Allemand, Thibaut 1 Auricchio, Gennaro 1 Bampi, Franco 1 Barbaini, Franco 1 Ben Abdallah, Naoufel 1 Cadum, Ennio 1 Carlen, Eric Anders 1 Cercignani, Carlo 1 Codegoni, Andrea 1 Della Croce, Lucia 1 Demichelis, Stefano 1 Duan, Renjun 1 Ferrari, Elisa 1 Filbet, Francis 1 Fornaro, Simona 1 Frommlet, Florian 1 Martínez Gamba, Irene 1 Gianazza, Ugo Pietro 1 Goudon, Thierry 1 Haskovec, Jan 1 Illner, Reinhard 1 Junca, Stéphane 1 Ladelli, Lucia 1 Li, Hailiang 1 Lisini, Stefano 1 Mouhot, Clément 1 Perthame, Benoît 1 Pietra, Paola 1 Polewczak, Jacek 1 Preziosi, Luigi 1 Rey, Thomas 1 Rionero, Salvatore 1 Rosado, Jesús 1 Scapolla, Terenzio 1 Silva, Santino 1 Van der Mee, Cornelis Victor Maria 1 Vecil, Francesco 1 Veneroni, Marco 1 Waluś, Włodzimierz all top 5 Serials 16 Journal of Statistical Physics 9 Kinetic and Related Models 8 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 7 Archive for Rational Mechanics and Analysis 7 Journal of Mathematical Physics 7 Transport Theory and Statistical Physics 5 Communications in Mathematical Physics 5 Monatshefte für Mathematik 5 SIAM Journal on Numerical Analysis 5 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 5 Communications in Mathematical Sciences 4 Physica A 4 Annali dell’Università di Ferrara. Nuova Serie. Sezione VII 4 Ricerche di Matematica 4 Comptes Rendus de l’Académie des Sciences. Série I 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Nonlinearity 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Applied Mathematics Letters 3 Continuum Mechanics and Thermodynamics 3 Communications on Applied Nonlinear Analysis 3 Istituto Lombardo, Accademia di Scienze e Lettere, Rendiconti, Sezione A 2 Computers & Mathematics with Applications 2 IEEE Transactions on Information Theory 2 Journal of Computational Physics 2 Mathematical Methods in the Applied Sciences 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Journal of Functional Analysis 2 Meccanica 2 Numerische Mathematik 2 Communications in Partial Differential Equations 2 SIAM Journal on Applied Mathematics 2 SIAM Journal on Mathematical Analysis 2 Discrete and Continuous Dynamical Systems 2 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 2 Journal of Evolution Equations 2 Milan Journal of Mathematics 2 Rivista di Matematica della Università di Parma. Serie 7 2 Bollettino della Unione Matematica Italiana. Series V. B 2 Series on Advances in Mathematics for Applied Sciences 2 Networks and Heterogeneous Media 2 Rivista di Matematica della Università di Parma. New Series 1 Journal of Mathematical Biology 1 Ukraïns’kyĭ Matematychnyĭ Zhurnal 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Atti della Accademia Peloritana dei Pericolanti. Classe di Scienze Fisiche, Matemàtiche e Naturali 1 Bulletin of the Technical University of Istanbul 1 Indiana University Mathematics Journal 1 Le Matematiche 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the American Mathematical Society 1 Quarterly of Applied Mathematics 1 Transactions of the American Mathematical Society 1 Rendiconti del Seminario Matematico 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Acta Applicandae Mathematicae 1 Physica D 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Revista Matemática Iberoamericana 1 Asymptotic Analysis 1 IMRN. International Mathematics Research Notices 1 Surveys on Mathematics for Industry 1 Bollettino della Unione Matemàtica Italiana. Serie VI. A 1 Bollettino della Unione Matemàtica Italiana. Serie VI. B 1 Journal of Nonlinear Science 1 SIAM Journal on Scientific Computing 1 Physics of Fluids 1 Electronic Journal of Differential Equations (EJDE) 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Mathematical Biosciences and Engineering 1 Bollettino della Unione Matematica Italiana. Series V. A 1 Lecture Notes in Mathematics 1 Supplemento ai Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Quaderni di Matematica 1 Journal of Physics A: Mathematical and Theoretical 1 Bollettino dell’Unione Matematica Italiana. Series IX 1 Rivista di Matematica della Università di Parma. Serie 8 1 Journal of Theoretical Biology 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 1 Matematica, Cultura e Società. Rivista dell’Unione Matematica Italiana. Serie I 1 Modeling and Simulation in Science, Engineering and Technology all top 5 Fields 117 Statistical mechanics, structure of matter (82-XX) 112 Partial differential equations (35-XX) 93 Fluid mechanics (76-XX) 33 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 30 Probability theory and stochastic processes (60-XX) 21 Information and communication theory, circuits (94-XX) 19 Numerical analysis (65-XX) 16 Integral equations (45-XX) 11 Biology and other natural sciences (92-XX) 9 General and overarching topics; collections (00-XX) 8 Real functions (26-XX) 5 Functional analysis (46-XX) 5 Statistics (62-XX) 5 Systems theory; control (93-XX) 4 Difference and functional equations (39-XX) 3 Mechanics of deformable solids (74-XX) 2 Measure and integration (28-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Operator theory (47-XX) 2 Quantum theory (81-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Convex and discrete geometry (52-XX) 1 Computer science (68-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Operations research, mathematical programming (90-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 180 Publications have been cited 3,761 times in 1,854 Documents Cited by ▼ Year ▼ Asymptotic flocking dynamics for the kinetic Cucker-Smale model. Zbl 1223.35058Carrillo, J. A.; Fornasier, M.; Rosado, J.; Toscani, G. 218 2010 On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations. Zbl 0982.35113Arnold, Anton; Markowich, Peter; Toscani, Giuseppe; Unterreiter, Andreas 165 2001 Particle, kinetic, and hydrodynamic models of swarming. Zbl 1211.91213Carrillo, José A.; Fornasier, Massimo; Toscani, Giuseppe; Vecil, Francesco 144 2010 Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities. Zbl 0984.35027Carrillo, J. A.; Jüngel, A.; Markowich, P. A.; Toscani, G.; Unterreiter, A. 131 2001 Kinetic models of opinion formation. Zbl 1195.91128Toscani, Giuseppe 120 2006 Asymptotic \(L^1\)-decay of solutions of the porous medium equation to self-similarity. Zbl 0963.35098Carrillo, J. A.; Toscani, G. 116 2000 Interacting multiagent systems. Kinetic equations and Monte Carlo methods. Zbl 1330.93004Pareschi, Lorenzo; Toscani, Giuseppe 96 2014 Uniformly accurate diffusive relaxation schemes for multiscale transport equations. Zbl 0976.65091Jin, Shi; Pareschi, Lorenzo; Toscani, Giuseppe 89 2000 A kinetic flocking model with diffusion. Zbl 1213.35395Duan, Renjun; Fornasier, Massimo; Toscani, Giuseppe 77 2010 Diffusive relaxation schemes for multiscale discrete-velocity kinetic equations. Zbl 0938.35097Jin, Shi; Pareschi, Lorenzo; Toscani, Giuseppe 76 1998 The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation. Zbl 1223.35264Gianazza, Ugo; Savaré, Giuseppe; Toscani, Giuseppe 75 2009 Mathematical modeling of collective behavior in socio-economic and life sciences. Zbl 1200.91010 73 2010 Diffusive limit for finite velocity Boltzmann kinetic models. Zbl 0896.35109Lions, Pierre Louis; Toscani, Giuseppe 66 1997 Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell gas. Zbl 0958.82044Toscani, G.; Villani, C. 66 1999 On a kinetic model for a simple market economy. Zbl 1133.91474Cordier, Stephane; Pareschi, Lorenzo; Toscani, Giuseppe 65 2005 An asymptotic-preserving well-balanced scheme for the hyperbolic heat equations. Zbl 0996.65093Gosse, Laurent; Toscani, Giuseppe 61 2002 Long-time asymptotics of kinetic models of granular flows. Zbl 1116.82025Li, Hailiang; Toscani, Giuseppe 59 2004 One-dimensional kinetic models of granular flows. Zbl 0981.76098Toscani, Giuseppe 56 2000 Metrics for probability distributions and the trend to equilibrium for solutions of the Boltzmann equation. Zbl 1081.82616Gabetta, E.; Toscani, G.; Wennberg, B. 55 1995 Fluid dynamic description of flocking via the Povzner-Boltzmann equation. Zbl 1213.37121Fornasier, Massimo; Haskovec, Jan; Toscani, Giuseppe 52 2011 On the Cauchy problem for the nonlinear Boltzmann equation global existence uniqueness and asymptotic stability. Zbl 0561.35074Bellomo, N.; Toscani, G. 50 1985 Long-Time asymptotics for strong solutions of the thin film equation. Zbl 0990.35054Carrillo, J. A.; Toscani, G. 50 2002 Fokker-Planck equations in the modeling of socio-economic phenomena. Zbl 1362.35305Furioli, Giulia; Pulvirenti, Ada; Terraneo, Elide; Toscani, Giuseppe 50 2017 Mathematical topics in nonlinear kinetic theory. Zbl 0702.76005Bellomo, Nicola; Palczewski, Andrzej; Toscani, Giuseppe 48 1988 Relaxation schemes for nonlinear kinetic equations. Zbl 0897.76071Gabetta, E.; Pareschi, L.; Toscani, G. 48 1997 Propagation of smoothness and the rate of exponential convergence to equilibrium for a spatially homogeneous Maxwellian gas. Zbl 0927.76088Carlen, E. A.; Gabetta, E.; Toscani, G. 47 1999 Entropy production and the rate of convergence to equilibrium for the Fokker-Planck equation. Zbl 1034.82041Toscani, G. 45 1999 Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation. Zbl 0944.35066Toscani, G.; Villani, C. 40 1999 Contractive probability metrics and asymptotic behavior of dissipative kinetic equations. Zbl 1142.82018Carrillo, J. A.; Toscani, G. 39 2007 Fast spectral methods for the Fokker-Planck-Landau collision operator. Zbl 1052.82545Pareschi, L.; Russo, G.; Toscani, G. 38 2000 On the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds. Zbl 1034.82032Toscani, G.; Villani, C. 37 2000 On generalized Csiszár-Kullback inequalities. Zbl 1015.94003Unterreiter, Andreas; Arnold, Anton; Markowich, Peter; Toscani, Giuseppe 33 2000 Lagrangian numerical approximations to one-dimensional convolution-diffusion equations. Zbl 1122.76064Gosse, Laurent; Toscani, Giuseppe 33 2006 Exponential convergence toward equilibrium for homogeneous Fokker-Planck-type equations. Zbl 0922.35131Carrillo, J. A.; Toscani, G. 33 1998 Entropies and equilibria of many-particle systems: an essay on recent research. Zbl 1063.35109Arnold, A.; Carrillo, J. A.; Desvillettes, L.; Dolbeault, J.; Jüngel, A.; Lederman, C.; Markowich, P. A.; Toscani, G.; Villani, C. 31 2004 Space localization and well-balanced schemes for discrete kinetic models in diffusive regimes. Zbl 1130.82340Gosse, Laurent; Toscani, Giuseppe 30 2003 Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials. Zbl 1119.82318Bobylev, A. V.; Cercignani, C.; Toscani, G. 29 2003 On the logarithmic Sobolev inequality. (Sur l’inégalité logarithmique de Sobolev.) Zbl 0905.46018Toscani, Giuseppe 29 1997 Contractive metrics for a Boltzmann equation for granular gases: Diffusive equilibria. Zbl 1085.82008Bisi, M.; Carrillo, J. A.; Toscani, G. 28 2005 Kinetic models for the trading of goods. Zbl 1267.82049Toscani, Giuseppe; Brugna, Carlo; Demichelis, Stefano 28 2013 On steady distributions of kinetic models of conservative economies. Zbl 1138.91020Matthes, Daniel; Toscani, Giuseppe 28 2008 Identification of asymptotic decay to self-similarity for one-dimensional filtration equations. Zbl 1145.76048Gosse, Laurent; Toscani, Giuseppe 27 2006 Wasserstein metric and large-time asymptotics of nonlinear diffusion equations. Zbl 1089.76055Carrillo, J. A.; Toscani, G. 26 2005 On large time asymptotics for drift-diffusion-Poisson systems. Zbl 1017.82041Arnold, Anton; Markowich, Peter; Toscani, Giuseppe 24 2000 Mathematical topics in nonlinear kinetic theory II. The Enskog equation. Zbl 0733.76061Bellomo, N.; Lachowicz, M.; Polewczak, J.; Toscani, G. 24 1991 Wealth distribution and collective knowledge: a Boltzmann approach. Zbl 1353.91036Pareschi, L.; Toscani, G. 24 2014 Asymptotic properties of the inelastic Kac model. Zbl 1072.82030Pulvirenti, Ada; Toscani, Giuseppe 23 2004 Self-similarity and power-like tails in nonconservative kinetic models. Zbl 1134.82037Pareschi, Lorenzo; Toscani, Giuseppe 23 2006 Long-time behavior for a nonlinear fourth-order parabolic equation. Zbl 1077.35028Cáceres, María J.; Carrillo, J. A.; Toscani, G. 22 2005 First-order continuous models of opinion formation. Zbl 1128.91043Aletti, Giacomo; Naldi, Giovanni; Toscani, Giuseppe 21 2007 On the nonlinear Boltzmann equation in unbounded domains. Zbl 0661.76077Toscani, G. 21 1986 Asymptotic-preserving and well-balanced schemes for radiative transfer and the Rosseland approximation. Zbl 1120.65343Gosse, Laurent; Toscani, Giuseppe 21 2004 Exponential time decay of solutions to a nonlinear fourth-order parabolic equation. Zbl 1029.35033Jüngel, A.; Toscani, G. 20 2003 Global solution of the initial value problem for the Boltzmann equation near a local Maxwellian. Zbl 0665.76085Toscani, G. 20 1988 Spectral methods for the non cut-off Boltzmann equation and numerical grazing collision limit. Zbl 1106.65324Pareschi, L.; Toscani, G.; Villani, C. 19 2003 Improved interpolation inequalities, relative entropy and fast diffusion equations. Zbl 1450.46020Dolbeault, Jean; Toscani, Giuseppe 19 2013 Decay rates in probability metrics towards homogeneous cooling states for the inelastic Maxwell model. Zbl 1135.82028Bisi, M.; Carrillo, J. A.; Toscani, G. 18 2006 The concavity of Rényi entropy power. Zbl 1360.94169Savaré, Giuseppe; Toscani, Giuseppe 18 2014 On the initial value problem for the Boltzmann equation with a force term. Zbl 0699.35237Bellomo, N.; Lachowicz, M.; Palczewski, A.; Toscani, G. 17 1989 Kinetic and hydrodynamic models of nearly elastic granular flows. Zbl 1136.82366Toscani, Giuseppe 17 2004 Poincaré inequalities for linearizations of very fast diffusion equations. Zbl 1011.35025Carrillo, J. A.; Lederman, C.; Markowich, P. A.; Toscani, G. 17 2002 The Enskog-Boltzmann equation in the whole space \({\mathbb{R}}^ 3:\) Some global existence, uniqueness and stability results. Zbl 0633.35072Toscani, G.; Bellomo, N. 16 1987 The theory of the nonlinear Boltzmann equation for Maxwell molecules in Fourier representation. Zbl 0874.45005Pulvirenti, A.; Toscani, G. 16 1996 Strict contractivity of the 2-Wasserstein distance for the porous medium equation by mass-centering. Zbl 1125.35053Carrillo, J. A.; Di Francesco, M.; Toscani, G. 16 2007 Exponential decay in time of solutions of the viscous quantum hydrodynamic equations. Zbl 1042.82047Gualdani, M. P.; Jüngel, A.; Toscani, G. 15 2003 Stability results for logarithmic Sobolev and Gagliardo-Nirenberg inequalities. Zbl 1355.46038Dolbeault, Jean; Toscani, Giuseppe 15 2016 Kinetic models of conservative economies with wealth redistribution. Zbl 1188.91115Bisi, Marzia; Spiga, Giampiero; Toscani, Giuseppe 14 2009 Finite speed of propagation in porous media by mass transportation methods. Zbl 1049.35110Carrillo, José Antonio; Gualdani, Maria Pia; Toscani, Giuseppe 14 2004 Call center service times are lognormal: a Fokker-Planck description. Zbl 1398.35247Gualandi, Stefano; Toscani, Giuseppe 13 2018 A strengthened central limit theorem for smooth densities. Zbl 0822.60018Lions, Pierre Louis; Toscani, Giuseppe 13 1995 Fourier-based distances and Berry-Esseen like inequalities for smooth densities. Zbl 0992.60027Goudon, Thierry; Junca, Stéphane; Toscani, Giuseppe 13 2002 The dissipative linear Boltzmann equation for hard spheres. Zbl 1103.82023Lods, Bertrand; Toscani, Giuseppe 13 2004 Remarks on entropy and equilibrium states. Zbl 0940.35168Toscani, G. 13 1999 Human behavior and lognormal distribution. A kinetic description. Zbl 1427.35280Gualandi, Stefano; Toscani, Giuseppe 13 2019 A Boltzmann-type approach to the formation of wealth distribution curves. Zbl 1189.91097Düring, Bertram; Matthes, Daniel; Toscani, Giuseppe 12 2009 A Boltzmann-like equation for choice formation. Zbl 1180.35402Comincioli, Valeriano; Della Croce, Lucia; Toscani, Giuseppe 12 2009 An information-theoretic proof of Nash’s inequality. Zbl 1301.62006Toscani, Giuseppe 12 2013 Finite time blow up in Kaniadakis-Quarati model of Bose-Einstein particles. Zbl 1252.35264Toscani, Giuseppe 12 2012 Kinetic approach to long time behavior of linearized fast diffusion equations. Zbl 1131.82030Cáceres, María J.; Toscani, Giuseppe 11 2007 The dissipative linear Boltzmann equation. Zbl 1083.82027Spiga, G.; Toscani, G. 11 2004 Kinetic modeling of alcohol consumption. Zbl 1431.35209Dimarco, Giacomo; Toscani, Giuseppe 11 2019 Nonlinear diffusions: extremal properties of Barenblatt profiles, best matching and delays. Zbl 1334.35098Dolbeault, Jean; Toscani, Giuseppe 11 2016 On the generalization of the Boltzmann \(H\)-theorem for spatially homogeneous Maxwell gas. Zbl 0825.76713Bobylev, A. V.; Toscani, G. 10 1992 Over-populated tails for conservative-in-the-mean inelastic Maxwell models. Zbl 1163.82008Carrillo, José A.; Cordier, Stéphane; Toscani, Giuseppe 10 2009 The grazing collision limit of the inelastic Kac model around a Lévy-type equilibrium. Zbl 1387.76094Furioli, G.; Pulvirenti, A.; Terraneo, E.; Toscani, G. 10 2012 Fast diffusion equations: matching large time asymptotics by relative entropy methods. Zbl 1252.35065Dolbeault, Jean; Toscani, Giuseppe 10 2011 Non-Maxwellian kinetic equations modeling the dynamics of wealth distribution. Zbl 1444.35138Furioli, Giulia; Pulvirenti, Ada; Terraneo, Elide; Toscani, Giuseppe 10 2020 Relaxation schemes for partial differential equations and applications to degenerate diffusion problems. Zbl 1028.35104Naldi, Giovanni; Pareschi, Lorenzo; Toscani, Giuseppe 9 2002 Grad’s equations and hydrodynamics for weakly inelastic granular flows. Zbl 1187.76049Bisi, M.; Spiga, G.; Toscani, G. 9 2004 International and domestic trading and wealth distribution. Zbl 1158.91430Düring, B.; Toscani, G. 9 2008 Accurate numerical methods for the collisional motion of (heated) granular flows. Zbl 1288.76056Filbet, Francis; Pareschi, Lorenzo; Toscani, Giuseppe 9 2005 New a priori estimates for the spatially homogeneous Boltzmann equation. Zbl 0760.76081Toscani, G. 8 1992 Global existence uniqueness and stability of the nonlinear Boltzmann equation with almost general gas-particles interaction potential. Zbl 0642.76093Toscani, G.; Bellomo, N. 8 1985 Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi-elastic limit. Zbl 1046.76034Naldi, Giovanni; Pareschi, Lorenzo; Toscani, Giuseppe 8 2003 Exponential and algebraic relaxation in kinetic models for wealth distribution. Zbl 1181.91264Düring, B.; Matthes, D.; Toscani, G. 8 2008 Wealth distribution in presence of debts: a Fokker-Planck description. Zbl 1388.91137Torregrossa, Marco; Toscani, Giuseppe 8 2018 Rényi entropy and improved equilibration rates to self-similarity for nonlinear diffusion equations. Zbl 1307.35141Carrillo, J. A.; Toscani, G. 8 2014 Hydrodynamic models of preference formation in multi-agent societies. Zbl 1427.35156Pareschi, Lorenzo; Toscani, Giuseppe; Tosin, Andrea; Zanella, Mattia 8 2019 Kinetic approach to the asymptotic behaviour of the solution to diffusion equations. Zbl 0904.35029Toscani, G. 7 1996 Convergence towards equilibrium for a gas of Maxwellian pseudomolecules. Zbl 0760.76082Toscani, G. 7 1992 Control of tumor growth distributions through kinetic methods. Zbl 1460.92057Preziosi, Luigi; Toscani, Giuseppe; Zanella, Mattia 5 2021 Kinetic models for epidemic dynamics with social heterogeneity. Zbl 1467.92189Dimarco, G.; Perthame, B.; Toscani, G.; Zanella, M. 4 2021 Entropy-type inequalities for generalized gamma densities. Zbl 1473.35575Toscani, Giuseppe 3 2021 Social contacts, epidemic spreading and health system. Mathematical modeling and applications to COVID-19 infection. Zbl 1471.92367Zanella, Mattia; Bardelli, Chiara; Azzi, Mara; Deandrea, Silvia; Perotti, Pietro; Silva, Santino; Cadum, Ennio; Figini, Silvia; Toscani, Giuseppe 1 2021 Non-Maxwellian kinetic equations modeling the dynamics of wealth distribution. Zbl 1444.35138Furioli, Giulia; Pulvirenti, Ada; Terraneo, Elide; Toscani, Giuseppe 10 2020 Social climbing and Amoroso distribution. Zbl 1451.35222Dimarco, Giacomo; Toscani, Giuseppe 4 2020 Kinetic modelling of multiple interactions in socio-economic systems. Zbl 1451.35103Toscani, Giuseppe; Tosin, Andrea; Zanella, Mattia 3 2020 Human behavior and lognormal distribution. A kinetic description. Zbl 1427.35280Gualandi, Stefano; Toscani, Giuseppe 13 2019 Kinetic modeling of alcohol consumption. Zbl 1431.35209Dimarco, Giacomo; Toscani, Giuseppe 11 2019 Hydrodynamic models of preference formation in multi-agent societies. Zbl 1427.35156Pareschi, Lorenzo; Toscani, Giuseppe; Tosin, Andrea; Zanella, Mattia 8 2019 Wright-Fisher-type equations for opinion formation, large time behavior and weighted logarithmic-Sobolev inequalities. Zbl 1434.35238Furioli, Giulia; Pulvirenti, Ada; Terraneo, Elide; Toscani, Giuseppe 5 2019 Poincaré-type inequalities for stable densities. Zbl 1422.60038Toscani, Giuseppe 1 2019 The information-theoretic meaning of Gagliardo-Nirenberg type inequalities. Zbl 1423.35136Toscani, Giuseppe 1 2019 Call center service times are lognormal: a Fokker-Planck description. Zbl 1398.35247Gualandi, Stefano; Toscani, Giuseppe 13 2018 Wealth distribution in presence of debts: a Fokker-Planck description. Zbl 1388.91137Torregrossa, Marco; Toscani, Giuseppe 8 2018 On a Fokker-Planck equation for wealth distribution. Zbl 1405.91180Torregrossa, Marco; Toscani, Giuseppe 5 2018 A Rosenau-type approach to the approximation of the linear Fokker-Planck equation. Zbl 1405.65100Toscani, Giuseppe 1 2018 Kinetic models for goods exchange in a multi-agent market. Zbl 07548931Brugna, Carlo; Toscani, Giuseppe 1 2018 Fokker-Planck equations in the modeling of socio-economic phenomena. Zbl 1362.35305Furioli, Giulia; Pulvirenti, Ada; Terraneo, Elide; Toscani, Giuseppe 50 2017 Score functions, generalized relative Fisher information and applications. Zbl 1374.60028Toscani, Giuseppe 3 2017 Stability results for logarithmic Sobolev and Gagliardo-Nirenberg inequalities. Zbl 1355.46038Dolbeault, Jean; Toscani, Giuseppe 15 2016 Nonlinear diffusions: extremal properties of Barenblatt profiles, best matching and delays. Zbl 1334.35098Dolbeault, Jean; Toscani, Giuseppe 11 2016 The fractional Fisher information and the central limit theorem for stable laws. Zbl 1366.60064Toscani, Giuseppe 6 2016 Condensation phenomena in nonlinear drift equations. Zbl 1355.35134Carrillo, José A.; Di Francesco, Marco; Toscani, Giuseppe 5 2016 Entropy inequalities for stable densities and strengthened central limit theorems. Zbl 1356.60039Toscani, Giuseppe 3 2016 Kinetic and mean field description of Gibrat’s law. Zbl 1400.91403Toscani, Giuseppe 1 2016 Boltzmann-type models for price formation in the presence of behavioral aspects. Zbl 1342.35204Brugna, Carlo; Toscani, Giuseppe 5 2015 Best matching Barenblatt profiles are delayed. Zbl 1311.35132Dolbeault, Jean; Toscani, Giuseppe 4 2015 Mean field dynamics of interaction processes with duplication, loss and copy. Zbl 1334.92329Bassetti, Federico; Toscani, Giuseppe 4 2015 A strengthened entropy power inequality for log-concave densities. Zbl 1359.94371Toscani, Giuseppe 3 2015 On Rosenau-type approximations to fractional diffusion equations. Zbl 1332.35379Furioli, Giulia; Pulvirenti, Ada; Terraneo, Elide; Toscani, Giuseppe 3 2015 Interacting multiagent systems. Kinetic equations and Monte Carlo methods. Zbl 1330.93004Pareschi, Lorenzo; Toscani, Giuseppe 96 2014 Wealth distribution and collective knowledge: a Boltzmann approach. Zbl 1353.91036Pareschi, L.; Toscani, G. 24 2014 The concavity of Rényi entropy power. Zbl 1360.94169Savaré, Giuseppe; Toscani, Giuseppe 18 2014 Rényi entropy and improved equilibration rates to self-similarity for nonlinear diffusion equations. Zbl 1307.35141Carrillo, J. A.; Toscani, G. 8 2014 Explicit equilibria in bilinear kinetic models for socio-economic interactions. Zbl 1335.91049Bassetti, Federico; Toscani, Giuseppe 6 2014 Rényi entropies and nonlinear diffusion equations. Zbl 1308.94044Toscani, Giuseppe 5 2014 Heat equation and convolution inequalities. Zbl 1303.26023Toscani, Giuseppe 4 2014 Kinetic models for the trading of goods. Zbl 1267.82049Toscani, Giuseppe; Brugna, Carlo; Demichelis, Stefano 28 2013 Improved interpolation inequalities, relative entropy and fast diffusion equations. Zbl 1450.46020Dolbeault, Jean; Toscani, Giuseppe 19 2013 An information-theoretic proof of Nash’s inequality. Zbl 1301.62006Toscani, Giuseppe 12 2013 A kinetic description of mutation processes in bacteria. Zbl 1321.92071Toscani, Giuseppe 5 2013 Large-time behavior of the solutions to Rosenau-type approximations to the heat equation. Zbl 1278.35022Rey, Thomas; Toscani, Giuseppe 2 2013 Finite time blow up in Kaniadakis-Quarati model of Bose-Einstein particles. Zbl 1252.35264Toscani, Giuseppe 12 2012 The grazing collision limit of the inelastic Kac model around a Lévy-type equilibrium. Zbl 1387.76094Furioli, G.; Pulvirenti, A.; Terraneo, E.; Toscani, G. 10 2012 Measure valued solutions of sub-linear diffusion equations with a drift term. Zbl 1267.35100Fornaro, Simona; Lisini, Stefano; Savaré, Giuseppe; Toscani, Giuseppe 3 2012 Variation on a theme by Bobylëv and Villani. Zbl 1245.82057Matthes, Daniel; Toscani, Giuseppe 1 2012 Fluid dynamic description of flocking via the Povzner-Boltzmann equation. Zbl 1213.37121Fornasier, Massimo; Haskovec, Jan; Toscani, Giuseppe 52 2011 Fast diffusion equations: matching large time asymptotics by relative entropy methods. Zbl 1252.35065Dolbeault, Jean; Toscani, Giuseppe 10 2011 Convex Sobolev inequalities derived from entropy dissipation. Zbl 1229.35302Matthes, Daniel; Jüngel, Ansgar; Toscani, Giuseppe 7 2011 On the minimization problem of sub-linear convex functionals. Zbl 1251.35168Ben Abdallah, Naoufel; Gamba, Irene M.; Toscani, Giuseppe 6 2011 Kinetic models with randomly perturbed binary collisions. Zbl 1220.82094Bassetti, Federico; Ladelli, Lucia; Toscani, Giuseppe 3 2011 The grazing collision limit of Kac caricature of Bose-Einstein particles. Zbl 1225.35241Allemand, Thibaut; Toscani, Giuseppe 2 2011 Asymptotic flocking dynamics for the kinetic Cucker-Smale model. Zbl 1223.35058Carrillo, J. A.; Fornasier, M.; Rosado, J.; Toscani, G. 218 2010 Particle, kinetic, and hydrodynamic models of swarming. Zbl 1211.91213Carrillo, José A.; Fornasier, Massimo; Toscani, Giuseppe; Vecil, Francesco 144 2010 A kinetic flocking model with diffusion. Zbl 1213.35395Duan, Renjun; Fornasier, Massimo; Toscani, Giuseppe 77 2010 Mathematical modeling of collective behavior in socio-economic and life sciences. Zbl 1200.91010 73 2010 Wealth redistribution in Boltzmann-like models of conservative economies. Zbl 1188.91164Toscani, Giuseppe; Brugna, Carlo 3 2010 Propagation of Sobolev regularity for a class of random kinetic models on the real line. Zbl 1203.82073Matthes, Daniel; Toscani, Giuseppe 3 2010 Convergence to self-similarity for the Boltzmann equation for strongly inelastic Maxwell molecules. Zbl 1425.82016Furioli, G.; Pulvirenti, A.; Terraneo, E.; Toscani, G. 1 2010 The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation. Zbl 1223.35264Gianazza, Ugo; Savaré, Giuseppe; Toscani, Giuseppe 75 2009 Kinetic models of conservative economies with wealth redistribution. Zbl 1188.91115Bisi, Marzia; Spiga, Giampiero; Toscani, Giuseppe 14 2009 A Boltzmann-type approach to the formation of wealth distribution curves. Zbl 1189.91097Düring, Bertram; Matthes, Daniel; Toscani, Giuseppe 12 2009 A Boltzmann-like equation for choice formation. Zbl 1180.35402Comincioli, Valeriano; Della Croce, Lucia; Toscani, Giuseppe 12 2009 Over-populated tails for conservative-in-the-mean inelastic Maxwell models. Zbl 1163.82008Carrillo, José A.; Cordier, Stéphane; Toscani, Giuseppe 10 2009 The diffusive limit of Carleman-type models in the range of very fast diffusion equations. Zbl 1239.35070Salvarani, Francesco; Toscani, Giuseppe 5 2009 Strong convergence towards self-similarity for one-dimensional dissipative Maxwell models. Zbl 1180.82150Furioli, G.; Pulvirenti, A.; Terraneo, E.; Toscani, G. 1 2009 On steady distributions of kinetic models of conservative economies. Zbl 1138.91020Matthes, Daniel; Toscani, Giuseppe 28 2008 International and domestic trading and wealth distribution. Zbl 1158.91430Düring, B.; Toscani, G. 9 2008 Exponential and algebraic relaxation in kinetic models for wealth distribution. Zbl 1181.91264Düring, B.; Matthes, D.; Toscani, G. 8 2008 Relaxation rate, diffusion approximation and Fick’s law for inelastic scattering Boltzmann models. Zbl 1144.35348Lods, Bertrand; Mouhot, Clément; Toscani, Giuseppe 7 2008 Analysis of a model for wealth redistribution. Zbl 1148.35304Matthes, Daniel; Toscani, Giuseppe 4 2008 Hydrodynamics from the dissipative Boltzmann equation. Zbl 1298.76212Toscani, Giuseppe 3 2008 Contractive probability metrics and asymptotic behavior of dissipative kinetic equations. Zbl 1142.82018Carrillo, J. A.; Toscani, G. 39 2007 First-order continuous models of opinion formation. Zbl 1128.91043Aletti, Giacomo; Naldi, Giovanni; Toscani, Giuseppe 21 2007 Strict contractivity of the 2-Wasserstein distance for the porous medium equation by mass-centering. Zbl 1125.35053Carrillo, J. A.; Di Francesco, M.; Toscani, G. 16 2007 Kinetic approach to long time behavior of linearized fast diffusion equations. Zbl 1131.82030Cáceres, María J.; Toscani, Giuseppe 11 2007 Kinetic models of opinion formation. Zbl 1195.91128Toscani, Giuseppe 120 2006 Lagrangian numerical approximations to one-dimensional convolution-diffusion equations. Zbl 1122.76064Gosse, Laurent; Toscani, Giuseppe 33 2006 Identification of asymptotic decay to self-similarity for one-dimensional filtration equations. Zbl 1145.76048Gosse, Laurent; Toscani, Giuseppe 27 2006 Self-similarity and power-like tails in nonconservative kinetic models. Zbl 1134.82037Pareschi, Lorenzo; Toscani, Giuseppe 23 2006 Decay rates in probability metrics towards homogeneous cooling states for the inelastic Maxwell model. Zbl 1135.82028Bisi, M.; Carrillo, J. A.; Toscani, G. 18 2006 Intermediate asymptotics beyond homogeneity and self-similarity: long time behavior for \(u_t = \Delta\varphi(u)\). Zbl 1096.35015Carrillo, José A.; Di Francesco, Marco; Toscani, Giuseppe 6 2006 On a kinetic model for a simple market economy. Zbl 1133.91474Cordier, Stephane; Pareschi, Lorenzo; Toscani, Giuseppe 65 2005 Contractive metrics for a Boltzmann equation for granular gases: Diffusive equilibria. Zbl 1085.82008Bisi, M.; Carrillo, J. A.; Toscani, G. 28 2005 Wasserstein metric and large-time asymptotics of nonlinear diffusion equations. Zbl 1089.76055Carrillo, J. A.; Toscani, G. 26 2005 Long-time behavior for a nonlinear fourth-order parabolic equation. Zbl 1077.35028Cáceres, María J.; Carrillo, J. A.; Toscani, G. 22 2005 Accurate numerical methods for the collisional motion of (heated) granular flows. Zbl 1288.76056Filbet, Francis; Pareschi, Lorenzo; Toscani, Giuseppe 9 2005 A central limit theorem for solutions of the porous medium equation. Zbl 1082.35091Toscani, Giuseppe 5 2005 Large-time asymptotics for nonlinear diffusions: the initial-boundary value problem. Zbl 1076.35057Salvarani, F.; Toscani, G. 2 2005 Long-time asymptotics of kinetic models of granular flows. Zbl 1116.82025Li, Hailiang; Toscani, Giuseppe 59 2004 Entropies and equilibria of many-particle systems: an essay on recent research. Zbl 1063.35109Arnold, A.; Carrillo, J. A.; Desvillettes, L.; Dolbeault, J.; Jüngel, A.; Lederman, C.; Markowich, P. A.; Toscani, G.; Villani, C. 31 2004 Asymptotic properties of the inelastic Kac model. Zbl 1072.82030Pulvirenti, Ada; Toscani, Giuseppe 23 2004 Asymptotic-preserving and well-balanced schemes for radiative transfer and the Rosseland approximation. Zbl 1120.65343Gosse, Laurent; Toscani, Giuseppe 21 2004 Kinetic and hydrodynamic models of nearly elastic granular flows. Zbl 1136.82366Toscani, Giuseppe 17 2004 Finite speed of propagation in porous media by mass transportation methods. Zbl 1049.35110Carrillo, José Antonio; Gualdani, Maria Pia; Toscani, Giuseppe 14 2004 The dissipative linear Boltzmann equation for hard spheres. Zbl 1103.82023Lods, Bertrand; Toscani, Giuseppe 13 2004 The dissipative linear Boltzmann equation. Zbl 1083.82027Spiga, G.; Toscani, G. 11 2004 Grad’s equations and hydrodynamics for weakly inelastic granular flows. Zbl 1187.76049Bisi, M.; Spiga, G.; Toscani, G. 9 2004 Modelling and numerical methods for granular gases. Zbl 1106.82032Pareschi, Lorenzo; Toscani, Giuseppe 3 2004 ...and 80 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,807 Authors 110 Carrillo de la Plata, José Antonio 92 Toscani, Giuseppe 74 Ha, Seung-Yeal 61 Pareschi, Lorenzo 45 Dolbeault, Jean 37 Bellomo, Nicola 30 Choi, Young-Pil 25 Zanella, Mattia 24 Jüngel, Ansgar 21 Degond, Pierre 20 Dimarco, Giacomo 19 Matthes, Daniel 18 Jin, Shi 17 Desvillettes, Laurent 17 Martínez Gamba, Irene 16 Carlen, Eric Anders 16 Gabetta, Ester 16 Herty, Michael Matthias 16 Markowich, Peter Alexander 16 Mischler, Stéphane 16 Mouhot, Clément 16 Vauchelet, Nicolas 15 Albi, Giacomo 15 Di Francesco, Marco 15 Gosse, Laurent 15 Kim, Jeongho 15 Lachowicz, Mirosław 15 Tosin, Andrea 15 Vazquez, Juan Luis 15 Zhang, Xiongtao 14 Burger, Martin 14 Goudon, Thierry 14 Villani, Cédric 13 Buet, Christophe 13 Fellner, Klemens 13 Haskovec, Jan 13 Klar, Axel 13 Loss, Michael 13 McCann, Robert J. 13 Yang, Tong 12 Cañizo, José Alfredo 12 Esteban, Maria J. 12 Filbet, Francis 12 Hu, Jingwei 11 Berthon, Christophe 11 Bisi, Marzia 11 Fetecau, Razvan C. 11 Soler, Juan S. 11 Tse, Oliver 11 Wolfram, Marie-Therese 11 Yun, Seok-Bae 10 Arnold, Anton 10 Chen, Li 10 Düring, Bertram 10 Fagioli, Simone 10 Fornasier, Massimo 10 Knopoff, Damian A. 10 Perthame, Benoît 10 Peszek, Jan 10 Saintier, Nicolas 10 Zinsl, Jonathan 9 Blanchet, Adrien 9 Brezzi, Franco 9 Calvez, Vincent 9 Dong, Jiu-Gang 9 Fournier, Nicolas G. 9 Huang, Yanghong 9 Kim, Doheon 9 Lemou, Mohammed 9 Liu, Jianguo 9 Lods, Bertrand 9 Park, Jinyeong 9 Pinasco, Juan Pablo 9 Pulvirenti, Ada 9 Regazzini, Eugenio 9 Rey, Thomas 9 Salvarani, Francesco 9 Samaey, Giovanni 9 Savaré, Giuseppe 9 Turpault, Rodolphe 9 Winkler, Michael 9 Zhang, Xianwen 8 Bolley, François 8 Carvalho, Maria Conceição 8 Chen, Xiuqing 8 Després, Bruno 8 Duan, Renjun 8 Fischer, Julian 8 Furioli, Giulia 8 Ko, Dongnam 8 Tan, Changhui 8 Terraneo, Elide 8 Wennberg, Bernt 7 Amadori, Debora 7 Bae, Hyeong-Ohk 7 Bertozzi, Andrea Louise 7 Bobylev, Alexandre Vasiljévitch 7 Bonforte, Matteo 7 Chainais-Hillairet, Claire 7 Colombi, Annachiara ...and 1,707 more Authors all top 5 Cited in 252 Serials 131 M\(^3\)AS. 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