Scientific Publications
and recent talks
Author of Books
- N.BELLOMO, A.PALCZEWSKI, G.TOSCANI Mathematical Topics in Nonlinear
Kinetic Theories, World Scientific, Singapore (1988), pg. IX + 226
- N.BELLOMO, M.LACHOWICZ, J.POLEWCZAK, G.TOSCANI Mathematical Topics
in Nonlinear Kinetic Theory II: The Enskog
Equation, World Scientific, Singapore (1991), pg. X + 207
Editor of Books
- G. TOSCANI ,
V. BOFFI, S. RIONERO Eds. Mathematical Aspects of Fluid and Plasma
Dynamics, Lecture Notes in Mathematics n.1460, Springer Verlag, Berlin (1991), pg. 221
- V. BOFFI, F.
BAMPI, G. TOSCANI Eds. Nonlinear Kinetic Theory and Mathematical Aspects of Hyperbolic
Systems, World Scientific, Singapore (1992) pg. XI + 267
- G. TOSCANI, Guest Editor Transport Theory and Statistical
Physics Special Issue devoted to the Proceedings of the Second
International Workshop on Nonlinear Kinetic Theories and Mathematical
Aspects of Hyperbolic Systems 25 , n. 3-5 (1996) 263-592
- L. PARESCHI, G.RUSSO, G.TOSCANI Eds. Modelling and Numerics of Kinetic Dissipative Systems, Nova Science
Publishers, New York, (2005) pg. II + 230
- G.TOSCANI Ed. Kinetic Methods for Nonconservative
and Reacting Systems, QM n.16, Aracne Editrice, Roma, (2005) pg. 331
- G.NALDI, L.PARESCHI, G.TOSCANI Eds. Mathematical
Modeling of Collective Behavior in Socio-Economic and Life Sciences,
Birkhauser, Boston (2010) pg. X + 435
Recent Papers
- G. Savaré, G. Toscani,
The concavity of renyi entropy power, (preprint)
(2012) Download
- G. Toscani, Heat equation and the sharp
Young's inequality, Rend. Lincei Mat. Appl. 24, 83–93 (2013) Download
- T. Rey, G. Toscani, Large-time behavior
of the solutions to Rosenau type approximations
to the heat equation, SIAM J. Appl. Math. (in press) (2013) Download
- G. Toscani, C. Brugna,
S. Demichelis, Kinetic models for the trading of
goods, J Stat Phys, 151 , (2013) 549-566 Download
- J. Dolbeault, G. Toscani,
Improved interpolation inequalities, relative entropy and fast diffusion
equations, Ann. I. H. Poincaré – AN (2013) Download
- G. Toscani, An information-theoretic
proof of Nash's inequality, Rend. Lincei Mat. Appl., 24, (2013) 83-93 Download
- G. Toscani, Lyapunov
functionals for the heat equation and sharp
inequalities, Atti Acc. Peloritana Pericolanti,
Classe Sc. Fis. Mat. e
Nat., 91, 1-10, (2013) Download
- D. Matthes, G. Toscani,
Variation on a theme by Bobylev and Villani, C.R.Acad.Sci.
Paris, Ser. I,
350 (1-2) (2012) 107-110 Download
- G. Furioli, A. Pulvirenti, E.
Terraneo, G. Toscani, The grazing collision limit of the inelastic Kac model around a Lévy-type equilibrium. SIAM
J. Math. Anal.
44, 827-850 (2012) Download
- G. Toscani, Finite time blow up in Kaniadakis-Quarati model of Bose-Einstein particles. Comm. Part. Diff. Eqns. 37 (1) (2012)
77-87 Download
- S. Fornaro, S. Lisini,
G. Savaré, G. Toscani,
Measure valued solutions of sub-linear diffusion equations with a drift
term, Discrete and Continuous Dynamical Systems A., 32 (5) 1675-1707
(2012) Download
- G. Toscani, N. Ben Abdallah,
I. M. Gamba, On the minimization problem
of sub-linear convex functionals. Kinetic and related Models, 4
(4), (2011) 857-871 Download
- J. Dolbeault, G. Toscani,
Fast diffusion equations: Matching large time asymptotics
by relative entropy methods. Kinetic and related Models 4
(2011) 701-716 Download
- F. Bassetti, L. Ladelli,
G. Toscani: Kinetic models with randomly
perturbed binary collisions. J. Statist. Phys. 142
(4) (2011) 686-709 Download
- T. Allemand, G. Toscani,
The grazing collision limit of Kac caricature of
Bose-Einstein particles, Asymptotic Analysis, 72 (3-4) (2011) 201-229 Download
- D. Matthes, A. Juengel,
G.Toscani, Convex Sobolev
inequalities derived from entropy dissipation, Arch. Rat. Mech. Anal. 199 (2) (2011) 563-596 Download
- M. Fornasier, J. Haskovec, G. Toscani, Fluid
dynamic description of flocking via Povzner–Boltzmann equation, Physica D 240 (2011) 21-31 Download
- F. Bassetti,
G. Toscani, Explicit equilibria
in a kinetic model of gambling, Phys. Rev. E, 81, 066115 (2010) Download
- J. A. Carrillo, M. Fornasier, G. Toscani, F. Vecil,
Particle, Kinetic, and Hydrodynamic Models of Swarming, in
Mathematical Modeling of Collective Behavior in Socio-Economic and Life
Sciences, G. Naldi, L. Pareschi
and G. Toscani Eds. Birkhauser, Boston
(2010) 297-336 Download
- D. Matthes, G. Toscani,
Propagation of Sobolev regularity for a class of
random kinetic models on the real line, Nonlinearity 23 (2010)
2081-2100 Download
- R. Duan, M. Fornasier,
G. Toscani, A kinetic flocking model with
diffusion, Commun. Math. Phys. 300, (2010) 95–145
Download
- C. Brugna, G. Toscani,
Wealth redistribution in Boltzmann-like models of conservative economies,
in Econophysics & Economics of Games, Social
Choices and Quantitative Techniques, B. Basu,
B.K. Chackabarti, S.R. Chackavarty,
K. Gangopadhyay (Eds.) Springer Verlag, Milan (2010) 71-82 Download
- G. Furioli, A. Pulvirenti,
E. Terraneo, G. Toscani,
Convergence to self-similarity for the Boltzmann equation for strongly
inelastic Maxwell molecules, Annales de l'Institut Henri Poincaré
(C) Analyse Non Linéaire,
27, (2) (2010) 719-737 Download
- J.A. Carrillo, M. Fornasier, J. Rosado,
G. Toscani, Asymptotic flocking dynamics for the
kinetic Cucker-Smale model, SIAM J. Math. Anal. 42,
(1) (2010). 218-236 Download
- G. Toscani, Wealth redistribution in
conservative linear kinetic models with taxation, Europhysics
Letters 88 (1) (2009) 10007 Download
- M. Bisi, G. Spiga,
G. Toscani, Kinetic models of conservative
economies with wealth redistribution, Commun. Math. Sci. 7 (4)
(2009) 901-916 Download
- B. Duering, D. Matthes,
G.Toscani, A Boltzmann-type approach to the
formation of wealth distribution curves, (Notes of the Porto Ercole School, June 2008) Riv. Mat. Univ. Parma (1) 8
(2009) 199-261 Download
- G. Furioli, A. Pulvirenti,
E. Terraneo, G. Toscani,
Strong Convergence towards self-similarity for one-dimensional dissipative
Maxwell models, J. Funct. Anal. 257 (7)
(2009) 2291-2324 Download
- V. Comincioli, L. Della Croce, G. Toscani, A Boltzmann-like equation for choice
formation, Kinetic and related Models 2 (1) (2009) 135- 149 Download
- J.A. Carrillo, S. Cordier, G. Toscani, Over-populated tails for conservative-in-the-mean
inelastic Maxwell models, Discrete and Continuous Dynamical Systems A. 24
(1) (2009) 59-81 Download
- F. Salvarani, G. Toscani,
The diffusive limit of Carleman-type models in
the range of very fast diffusion equations, J.Evol.Equ.
9 (2009) 67-80 Download
- B. Duering, G.Toscani,
International and domestic trading and wealth distribution, Commun. Math. Sci. 6 (4)
(2008) 1043-1058 Download
- B. Duering, D. Matthes,
G.Toscani, Kinetic Equations modelling
Wealth Redistribution: A comparison of Approaches, Phys. Rev. E,
78, (2008) 056103 Download
- M. Bisi, G. Spiga,
G. Toscani, On the hydrodynamic closure of a
transport-diffusion equation, Europhysics
Letters 83, (2008) 40007 Download
- B. Lods, C. Mouhot,
G. Toscani, Relaxation rate, diffusion
approximation and Fick's law for inelastic
scattering Boltzmann models, Kinetic and related Models, 2 (2008)
223-248 Download
- B. Duering, D. Matthes,
G.Toscani, Exponential and algebraic relaxation
in kinetic models for wealth distribution, in Proceedings WASCOM 2007 N. Manganaro, R. Monaco, S. Rionero
Eds., World Scientific, Singapore 2008, 228-238 Download
- G. Toscani,
Funzionali entropia ed equilibrio di sistemi di molte particelle,
Bollettino UMI serie IX, Vol. 1 (3) (2008), 509-524 Download
- G. Toscani, Hydrodynamics from the dissipative
Boltzmann equation, in "Mathematical models of granular
matters" G. Capriz, P. Giovine
and P. M. Mariano Editors, Lecture Notes in Mathematics n.1937
(2008) 59-75 Download
- U. Gianazza, G. Savaré,
G. Toscani, The Wasserstein gradient flow of the
Fisher information and the quantum drift-diffusion equation, Arch. Rat. Mech. Anal. 194, (1) (2009) 133-220 Download
- D. Matthes, G.Toscani,
Analysis of a model for wealth redistribution, Kinetic and related Models,
1 (2008), 1-22 Download
- D. Matthes, G. Toscani,
On steady distributions of kinetic models of conservative economies, J.
Statist. Phys.,
130 (2008) 1087-1117 Download
- J.A. Carrillo, G. Toscani,
Contractive probability metrics ans asymptotic
behavior of dissipative kinetic equations (Notes of the Porto Ercole School, June 2006) Riv. Mat. Univ. Parma, (7)
6, (2007) 75-198 Download
- J.A. Carrillo, M. Di Francesco, G. Toscani,
Strict Contractivity of the 2-Wasserstein
distance for the porous medium equation by mass-centering, Proc. Amer. Math. Soc. 135 (2007), 353-363 Download
- B. Duering, G. Toscani,
Hydrodynamics from kinetic models of conservative economies, Physica A: Statistical Mechanics and its
Applications, 384 (2007) 493-506 Download
- M.J. Càceres, G. Toscani,
Kinetic approach to long time behavior of linearized
fast diffusion equations, J. Statist. Phys., 128 (4)
(2007) 883-925 Download
- G. Aletti, G. Naldi,
G. Toscani, First-order continuous models of
opinion formation, SIAM J. Appl. Math., 67 (3) (2007) 837-853 Download
- G. Toscani, Kinetic models of opinion
formation, Commun. Math. Sci. 4
(3) (2006) 481-496 Download
- M. Bisi, J.A. Carrillo, G. Toscani, Decay rates in probability metrics towards
homogeneous cooling states for the inelastic Maxwell model, J. Statist.Phys., 124 (2-4) (2006) 625-653 Download
- L. Pareschi, G. Toscani,
Self-similarity and power-like tails in nonconservative
kinetic models, J. Statist. Phys. 124 (2-4)
(2006) 747-779 Download
- L. Gosse, G. Toscani, Lagrangian
numerical approximations
to one-dimensional convolution-diffusion equations,
SIAM J. Sci. Comput., 28 (4) (2006)
1203-1227 Download
- M.P.Gualdani, A. Juengel, G.Toscani,
A nonlinear fourth-order parabolic equation with nonhomogeneous
boundary conditions, SIAM J. Math. Anal., 37 (6)
(2006) 1761-1779 Download
- L. Gosse, G. Toscani, Identification of
asymptotic decay to self-similarity for one-dimensional filtration
equations, SIAM J. Numer. Anal., 43
(6) (2006) 2590-2606 Download
- J.A. Carrillo, M. Di Francesco, G. Toscani,
Intermediate asymptotics beyond homogeneity and
self-similarity: long time behavior for nonlinear diffusions, Arch. Ration. Mech. Anal., 180 (1) (2006)
127-149 Download
- S. Cordier, L. Pareschi,
G. Toscani, On a kinetic model for a simple
market economy, J. Statist. Phys., 120 (2005) 253-277 Download
- M.J. Càceres, J.A. Carrillo, G.Toscani, Long-time behavior for a nonlinear fourth
order parabolic equation, Trans. Amer. Math.
Soc. 357 (2005) 1161-1175 Download
- M. Bisi, J.A. Carrillo, G. Toscani, Contractive
Metrics for a Boltzmann equation for granular gases:
Diffusive equilibria, J. Statist. Phys., 118 (1-2)
(2005) 301-331 Download
- F. Filbet, L. Pareschi,
G. Toscani, Accurate numerical methods for the collisional motion of (heated) granular flows, J. Comput. Phys. 202,
(1) ( 2005) 216-235 Download
- B. Lods, G. Toscani,
Long time behavior of non--autonomous Fokker--Planck equations and the
cooling of granular gases., Ukrainian Math. J., 57 (6) 778-789 (2005) Download
- F. Salvarani, G. Toscani,
Large-time asymptotics for nonlinear diffusions:
the initial-boundary value problem, J. Math. Phys. 46,
023502 (2005) (11 pages) Download
- G. Toscani, A central limit theorem for
solutions of the porous medium equation, J. Evol.
Equ. 5 (2005) 185-203 Download
- J.A. Carrillo, G. Toscani, Wasserstein
metric and large-time asymptotics of nonlinear
diffusion equations, in New trends in mathematical physics, World
Sci. Publ., Hackensack,
NJ, (2004) 234–244. Download
Recent Talks
- Kinetic and Hydrodynamic Models of flocking phenomena Download
- Kinetic models of Maxwell type. A brief history. Part I Download
- Kinetic models of Maxwell type. A brief history. Part II Download
- Formation of tails in nonconservative
kinetic models Download
- Kinetic models of economy. The conservative case Download
- Kinetic models of opinion formation Download
Papers
- [1] F.Barbaini, G.Toscani, Costruzione di misure mediante tempi
d'arresto, Rend. Ist.
Lombardo, 1(A) 109, (1975) 49-64
- [2] I.Guarneri,
G.Toscani, Statistical equilibrium of a
classical, randomly driven radiating system, Lett. Nuovo Cimento 14, n.3, serie 2 (1975) 101-107
- [3] I.Guarneri, G.Toscani, Stochastic electrodynamics of a one-dimensional cavity,
Bollettino UMI 1(5) 14-B (1977) 31-41
- [4] C.Bertoluzza, G.Toscani, Caratterizzazione della legge di
composizione d'esperienza per misure d'informazione idempotenti,
Rend. Ist. Lombardo
1(A) 112 (1978) 99-109
- [5] C.Bertoluzza, G.Toscani, Diramativit`a
generalizzata e leggi di composizione in teoria dell'informazione, Rend. Ist. Lombardo 1(A) 113
(1979) 84-91
- [6] E.Gabetta, G.Toscani, Multiple random scattering in one dimension, Bollettino UMI 1(5) 17-B (1980) 1047-1062
- [7] G.Toscani,
An approach to white-noise via wide-sense stationary processes with
piecewise constant sample functions, Bollettino
UMI 118-A (1981) 309-315
- [8] E.Gabetta,
G.Toscani, Stochastic stability of a class of
linear dynamical systems, Rend. Sem. Mat. Univ.
Polit. Torino 40 (2) (1981) 53-62
- [9] G.Toscani,
Products of independent random processes and gaussian
white-noise, Rend. Sem. Mat. Univ.
Polit. Torino, Special
Issue (1982) 233-239
- [10] G.Toscani, Sums of independent
random processes,
Bollettino UMI 1(6) 1-A (1982) 241-248
- [11] G.Toscani, Random motion of a perfectly inelastic particle, Atti VI Congr. Naz. AIMETA,
Genova (1982), 1, 268-276
- [12] G.Toscani, Solution globale du modele a vitesse discrète de
l'équation de Boltzmann
en théorie cinetique, C.R.A.S. t.296 Serie 1 (1983) 577-580
- [13] G.Toscani,
On the discrete velocity models of the Boltzmann equation in several
dimensions, Ann. Matem. Pura Appl. Vol.CXXXVIII (1984) 279-308
- [14] N.Bellomo, R.Illner, G.Toscani, Sur le problème de Cauchy pour l'équation de Boltzmann semi-discrète, C.R.A.S.
t.299, Serie I (1984) 835-839
- [15] G.Toscani, On the
semidiscrete Boltzmann equation,
Atti VII Congr. Naz. AIMETA, Trieste (1984), 1,
85-89
- [16] N.Bellomo,
G.Toscani, On the Cauchy problem for the
nonlinear Boltzmann equation:global existence,uniqueness, and asymptotic behaviour, J. Math. Phys.
12 (1985) 340-345
- [17] G.Toscani,
On the asymptotic behaviour and stability of the
solution for the Broadwell model of the
Boltzmann equation in three dimensions, Math. Meth. in Appl. Sc. 17 (1985)
340-345
- [18] G.Toscani, Diffusion with collision of a perfectly inelastic particle, Bollettino UMI 1(6) 4-B (1985) 801-812
- [19] G.Toscani,
Global existence and asymptotic behaviour for
the discrete velocity models of the Boltzmann equation, J. Math. Phys. 111 (1985) 2918-2921
- [20] G.Toscani,
N.Bellomo Global existence,uniqueness
and stability of the nonlinear Boltzmann equation with almost general
gas-particle interaction potential, Rend. Circolo Matem. Palermo,
Suppl. Serie II, n.8 (1985) 419-433
- [21] G.Toscani,
The semidiscrete Boltzmann equation for
hard-spheres, Meccanica 120 (1985) 249-252
- [22] G.Toscani,
Global existence and asymptotic behaviour for
the discrete velocity models of the Boltzmann equation, Quaderni del CNR, GNFM Proceedings of Workshop on
Mathematical Aspects of Fluid and Plasma Dynamics, C.Cercignani,
S.Rionero, M.Tessarotto
Eds., (1985) 565-573
- [23] N.Bellomo,
G.Toscani, On the Cauchy problem for the
nonlinear Boltzmann equation: global existence, uniqueness and asymptotic
stability, Quaderni del CNR, GNFM Proceedings of
Workshop on Mathematical Aspects of Fluid and Plasma Dynamics, C.Cercignani, S.Rionero, M.Tessarotto Eds., (1985) 45-60
- [24] G.Toscani,
On the nonlinear Boltzmann equation in unbounded domains, Arch. Ration. Mech. Anal.
195 (1986) 37-49
- [25] V.Protopopescu, G.Toscani, Existence globale
pour un problème mixte
associè á l'équation
de Boltzmann non-lineaire,
C.R.A.S. t.302 Serie I, n.6 (1986) 255-258
- [26] N.Bellomo,
G.Toscani, The nonlinear Boltzmann equation:
analysis of the influence of the cut-off on the solution of the Cauchy
problem, XV Int. Symposium on R.G.D., B.G.Teubner
Editor Vol.I (1986) 167-174
- [27] N.Bellomo,
G.Toscani, Lecture notes on the Cauchy problem
for the nonlinear Boltzmann equation, Internal Report Dip. Matem. Polit. Torino, Levrotto & Bella Editors
(1986) 1-101
- [28] G.Toscani,
New results on the Boltzmann equation in unbounded domains, Trans. Theory and Stat. Phys. 116 (2-3) (1987) 223-230
- [29] N.Bellomo,
G.Toscani, On theEnskog-Boltzmann
equation in the whole space R3 :Some global existence,uniqueness
and stability results, Comput. Math. Applic. 13 n.9-11 (1987)
851-859
- [30] G.Toscani,
V.Protopopescu, The nonlinear Boltzmann equation
with partially absorbing boundary conditions. Global existence and uniqueness results, J. Math. Phys. 128 (1987)
1140-1145
- [31] G.Toscani,
H-theorem and asymptotic trend to equilibrium for a rarefied gas in the
vacuum, Arch. Ration. Mech. Anal.100
(1987) 1-12
- [32] R.Monaco,
G.Toscani, New results on the semidiscrete Boltzmann equation for a binary gas
mixture, Meccanica 122 (1987) 179-184
- [33] G.Toscani,
Global solutions to the Boltzmann equation near a local Maxwellian, Rend. Sem. Mat. Univ. Pol. Torino, Fasc.Spec. Hyperbolic Equations (1988)
279-286
- [34] G.Toscani,
C.V.M.Vandermee An abstract approach to
nonlinear Boltzmann type equations, Ann. Univ.
Ferrara Sez.7, Vol. XXXIV (1988) 75-100
- [35] G.Toscani,
Global solutions of the initial value problem for the Boltzmann equation
near a local Maxwellian, Arch. Ration. Mech. Anal.
102 (1988) 231-241
- [36] G.Toscani,
On the Cauchy problem for the discrete Boltzmann equation with initial
values in L1( R+), Commun. Math. Phys. 1121 (1989) 121-142
- [37] N.Bellomo,
G.Toscani, On the Enskog-Boltzmann
equation in unbounded domains: some global existence and stability results
Proceedings of III Meeting on Waves and Stability in Continuous Media,
Bari, 1985 M.Maiellaro, L.Palese
Eds., Bari (1989) 1-18
- [38] A.Palczewski,
G.Toscani, Global solution of the Boltzmann
equation for rigid spheres and initial data close to a local Maxwellian, J. Math. Phys.
430 (1989) 2445-2450
- [39] N.Bellomo,
M.Lachowicz, A.Palczewski,
G.Toscani, On the initial value problem for the
Boltzmann equation with a force term, Trans. Theory & Stat. Phys. 118 (1) (1989) 87-102
- [40] G.Toscani,
Recent developments on the existence theory for the discrete velocity
models, Proceedings of Discrete Kinetic Theory, Lattice Gas Dynamics and
Foundation of Hydrodynamics, Torino, 1988, R.Monaco
Ed. World Scientific,
Singapore (1989) 355-370
- [41] N.Bellomo,
G.Toscani, On the Cauchy problem for the discrete
Boltzmann equation with multiple collisions: existence, uniqueness and
stability, Stab. Meth. Appl. Anal.
in Continua 1 (1990) 165-184
- [42] G.Borgioli,
R.Monaco, G.Toscani,
On the semidiscrete Enskog
equation, Proceedings of the V Meeting on Waves and Stability in
Continuous Media, Sorrento, 1989, S.Rionero
Ed. World Scientific,
Singapore (1991) 34-40
- [43] G.Borgioli,
A.Pulvirenti, G.Toscani,
On the Cauchy problem for the semidiscrete Enskog equation, Proceedings of Advances in Kinetic
Theory and Continuoum Mechanics, R.Gatignol & Soubbaramayer
Eds., Springer Verlag, Berlin (1991) 91-98
- [44] G.Toscani,
W.Walus, Recent results on the fractional step
method in discrete kinetic theory, Proceedings of Discrete Models od Fluid Dynamics, Coimbra 1990, A.Alves
Ed., World Scientific, Singapore (1991) 123-130
- [45] G.Toscani,
Existence results for some nonlinear hyperbolic system from kinetic theory
of gases, Non linear hyperbolic equations and field theory, M.K.V.Murthy& L.Spagnolo
Eds. (1991) Pitman
Research Note Series
- [46] G.Toscani,
On the discrete Boltzmann equation with multiple collisions, Atti Accad. Peloritana
Pericolanti, Classe Sci. Fis. Mat. Nat. V. LXVIII, Suppl. 1 (1991) 441-457
- [47] G.Toscani,
W.Walus, The initial-boundary value problem for
the four velocity plane Broadwell model,
Math. Meth. and Models in Appl. Sci. 1 (1991) 293-310
- [48] G.Toscani,
On Shannon's entropy powers inequality, Ann. Univ. Ferrara, Sez. 7, Vol. XXXVII
(1991) 167--184
- [49] G.Toscani,
An inequality for convex functionals and its
application to a Maxwellian gas Le Matematiche, XLVI, 1 (1991) 481 491
- [50] G.Toscani,
Convergence towards equilibrium for a gas of Maxwellian
pseudomolecules, Cont. Mech. Termodyn. 4 (1992) 95-107
- [51] G.Toscani,
New a priori estimates for the spatially homogeneous Boltzmann equation,
Cont. Mech. Termodyn. 4 (1992) 81-93
- [52] G.Toscani,
A.V.Bobylev On the generalization of the
Boltzmann H-theorem for a spatially homogeneous Maxwell gas, J.
Math. Phys. 33 (1992), 2578--2586.
- [53] G.Toscani,
Lyapunov functionals
for a Maxwell gas, Arch. Ration.
Mech. Anal. 119 (1992)
301-307
- [54] V.Comincioli,
G.Toscani, Operator splitting of the Boltmann equation for a Maxwell gas in ``Boundary
Value Problems for Partial Differential Equations and Applications'', RMA
Res. Notes Appl. Math., 29 C.Baiocchi and J.L.Lions Eds., Masson Paris, (1993) 345--350
- [55] E.Gabetta,
G.Toscani, On convergence to equilibrium for Kac's caricature of a Maxwellian
gas, J. Math. Phys. 35, 1 (1994) 190-208
- [56] E.Gabetta,
G.Toscani, On entropy production rates for some
kinetic equations, Bull. Tech.
Univ. Istanbul 47, (1994) 219-230
- [57] G.Toscani, Bivariate distributions with given marginals and applications to kinetic theory of gases, Atti "Convegno Nazionale del Gruppo AIMETA
di Meccanica Stocastica'' E. Mascolino Ed., Messina (1994)
- [58] G.Toscani,
Strong convergence in Lp for a spatially
homogeneous Maxwell gas with cut-off, Transp. The.& Stat. Phys. 26 (1995) 319-328
- [59] P.L.Lions,
G.Toscani, A sthrenghtened
central limit theorem for smooth densities, J. Funct. Anal. 128 (1995) 148-167
- [60] V.Comincioli, G.Naldi, G.Toscani, Nonlinear diffusion and fluid dynamical limit from discrete velocity models, Comm. Appl. Nonlinear Anal. 2 (1995) 1-29
- [61] E.Gabetta,
G.Toscani, B.Wennberg
Metrics for probability distributions and the trend to equilibrium for
solutions of the Boltzmann equation J. Statist. Phys. 81 (1995) 901-934
- [62] A.Pulvirenti,
G.Toscani, The theory of nonlinear Botzmann equation for Maxwell molecules in Fourier
representation Ann. Matem. Pura Appl. Vol. CLXXI
(1996) 181-204
- [63] E. Gabetta,
L. Pareschi, G. Toscani,
Wild's sums and numerical approximation of nonlinear kinetic equations,
Transp. The. & Stat.
Phys. 25 (1996) 515-530
- [64] E.Gabetta,
G.Toscani, B.Wennberg
The Tanaka functional and exponential convergence for non cut-off
molecules, Transp. The.
& Stat. Phys. 25
(1996) 543-554
- [65] A.V. Bobylev,
G.Toscani, Two dimensional half-space problems
for the Broadwell discrete velocity model,
Continuum Mech. Thermodyn. 8, (1996) 257-274
- [66] G.Toscani,
Kinetic approach to the asymptotic behaviour of
the solution to diffusion equations Rendic. di Matem. Serie VII 16 (1996) 329-346
- [67] G.Toscani,
On regularity and asymptotic behaviour of a
spatially homogeneous Maxwell gas Rendiconti Circolo Mat. Palermo
Suppl. 45 (1996) 649-662
- [68] A. Pulvirenti, G.Toscani, Fast diffusion as a limit of a two-velocity kinetic model Rendiconti
Circolo Mat. Palermo Suppl. 45 (1996) 521-528
- [69] E. Gabetta,
L. Pareschi, G. Toscani,
Relaxation schemes for nonlinear kinetic equations, SIAM J. Numer. Anal.
34 (1997) 2168--2194
- [70] P.L.Lions, G.Toscani, Diffusive limits for finite velocity Boltzmann kinetic models, Revista Mat. Iberoamer. 13 (1997) 473--513
- [71] V.Comincioli,
G.Naldi, G.Toscani,
The diffusive limit of two velocity models: the porous medium equation,
Transp. The. & Stat.
Phys. 26 (1997) 49-63
- [72] G. Toscani, Sur l'inégalité logarithmique de Sobolev CRAS 324, S'erie I
(1997) 689-694
- [73] S. Jin, L. Pareschi, G. Toscani, Diffusive relaxation
schemes for multiscale discrete-velocity
kinetic equations,
SIAM J. Numer. Anal.
35 2405-2439 (1998)
- [74] A. Pulvirenti,
G. Toscani, On the grazing collision limit for
the spatially homogeneous Boltzmann equation Rendiconti
Circolo Mat. Palermo
Suppl. 57 (1998) 405-412
- [75] G. Toscani,
The grazing collisions asymptotics of the non
cut-off Kac equation, M2AN Math. Model. Numer. Anal.,
32 (1998) pp 763-772
- [76] J.A. Carrillo, G. Toscani, Exponential convergence toward equilibrium
for homogeneous Fokker-Planck-type equations, Math. Methods Appl. Sci., 21 (1998)
1269-1286
- [77] E.A. Carlen, E. Gabetta, G. Toscani,
Propagation of smoothness and the rate of exponential convergence to
equilibrium for a spatially homogeneous Maxwellian
gas, Commun. Math.
Phys. 199, 521-546 (1999).
- [78] G. Toscani,
C. Villani Probability metrics and uniqueness of
the solution to the Boltzmann equation for a Maxwell gas, J.
Statist. Phys., 94 619-637 (1999)
- [79] G. Naldi,
L. Pareschi, G. Toscani,
Hyperbolic relaxation approximation to nonlinear parabolic problems, on
International Series of Numerical Mathematics, 130 Birkhäuser
Verlag, Basel (1999) 747-756
- [80] G. Toscani,
C. Villani, Sharp entropy dissipation bounds and
explicit rate of trend to equilibrium for the spatially homogeneous
Boltzmann equation, Commun. Math. Phys. 203, (1999) 667-706
- [81] G. Toscani,
Entropy production and the rate of convergence to equilibrium for the
Fokker-Planck equation, Quarterly of Appl. Math.,
Vol. LVII (1999), 521-541
- [82] G. Toscani,
Remarks on entropy and equilibrium states, Appl. Math. Letters, 12 (1999) 19-25
- [83] S. Jin, L. Pareschi, G. Toscani,
Uniformly accurate diffusive relaxation schemes for multiscale
transport equations, SIAM J. Numerical Analysis 38, 13, (2000) pp. 913-936.
- [84] A. Arnold, P. Markowich, G. Toscani, On
large time asymptotics for
drift-diffusion-Poisson systems, Transport Theory Statist. Phys. 29 (2000), no. 3-5, 571--581.
- [85] L. Pareschi,
G. Russo, G. Toscani, Fast spectral methods for
the Fokker-Planck-Landau equation, J. Comput. Phys. 165 (2000), 216--236.
- [86] G. Toscani,
C. Villani, On the trend to equilibrium for some
dissipative systems with slowing increasing a priori bounds, J.
Statist. Phys., 98 (2000) 1279--1309
- [87] L. Pareschi, G.Russo, G. Toscani, Méthode
spéctrale rapide pour l'équation
de Fokker-Planck-Landau, CRAS 330, Série I,
(2000) 517--522
- [88] J. A. Carrillo, G. Toscani, Asymptotic L1-decay of the porous medium
equation to self-similarity , Indiana Univ. Math. J., 46 (2000), 113--142
- [89] A. Arnold, P. Markowich, G. Toscani, A. Unterreiter, On generalized Csiszar--Kullback inequalities, Monatschefte
für Mathematik, 131,
(2000) 235--253,
- [90] G. Toscani,
One-dimensional kinetic models with dissipative collisions, M2AN
Math. Model. Numer. Anal.,
34 (2000), 1277-1292
- [91] V. Comincioli,
G. Naldi, L. Pareschi,
G. Toscani, Numerical methods for multiscale hyperbolic systems and nonlinear parabolic
equations, Ann. Univ. Ferrara, Sez. 7, Vol. XLV Suppl., (2000) 255--266
- [92] G. Naldi,
L. Pareschi, G. Toscani,
Convergence of kinetic approximation to nonlinear parabolic
problems, in Godunov Methods (Oxford 1999), E.F. Toro (Editor),
655--662 Kluwer/ Plenum Publishers, New
York (2001)
- [93] A. Jüngel,
P.A. Markowich, G. Toscani,
Decay rates for solutions of degenerate parabolic systems, Electron. J. Diff. Eqns.,
Conf. 06, (2001), pp. 189-202.
- [94] A. Arnold, P. Markowich, G. Toscani, A. Unterreiter, On convex Sobolev
inequalities and the rate of convergence to equilibrium for Fokker-Planck
type equations, Commun. Partial Diff. Equa. 26 (2001), 43-100
- [95] J.A. Carrillo, A. Jüngel, P.A. Markowich, G. Toscani, A. Unterreiter,
Entropy dissipation methods for degenerate parabolic equations and systems
and generalized Sobolev inequalities, Monatschefte für Mathematik, 133 (2001), 1-82
- [96] J.L. Lopez, J. Soler, G. Toscani, Time
rescaling and asymptotic behavior of some fourth order degenerate
diffusion equations, Comput. Math. Appl., 43 (2002) 721-736
- [97] G. Naldi,
L. Pareschi, G. Toscani,
Relaxation schemes for partial differential equations and applications to
degenerate diffusion problems, Surv. Math. Ind. 10, (2002) 315--343
- [98] V. Comincioli, G. Naldi, T. Scapolla, G.
Toscani, Multiscale hyperbolic
equations: numerical approximation in the diffusive regime, in Recent Trends in Numerical Analysis, L. Brugnano& D. Trigiante Eds. Nova Science Publishers,
(2001)
- [99] J.A. Carrillo, G. Toscani, Long-Time asymptotics
for strong solutions of the thin film equation, Commun. Math. Phys., 225 (2002) 551-571
- [100] J.A. Carrillo, C.
Lederman, P.A. Markowich and G. Toscani, Poincare Inequalities for Linearizations
of Very Fast Diffusion Equations, Nonlinearity 15, (2002) 565-580
- [101] T. Goudon,
S. Junca, G. Toscani,
Fourier-based distances and Berry-Esseen like
inequalities for smooth densities, Monatschefte
für Mathematik, 135
(2002) 115-136
- [102] O. Klein, G. Toscani, Scaling properties of operators and
entropies, (preprint) (2001)
- [103] L. Gosse, G. Toscani, An asymptotic preserving well-balanced scheme
for the hyperbolic heat equation, CRAS Série I,
334 (2002) 1-6
- [104] L. Gosse, G. Toscani, Space localization and well-balanced scheme
for discrete kinetic models in diffusive regimes, SIAM J. Numer. Anal.
41, (2) (2003) 641-658
- [105] G. Naldi, L. Pareschi, G. Toscani, Spectral methods for one-dimensional kinetic
models of granular flows and numerical quasi-elastic limit, M2AN
Math. Model. Numer. Anal.,
37, (2003) 73-90
- [106] A. Jüngel,
G. Toscani, Decay rates of solutions to a
nonlinear fourth--order parabolic equation, Z. Angew. Math. Phys. 54, (2003) 377-386
- [107] F. Frommlet, J.L. López, J. Soler, G. Toscani, Nonlinear
rescaling, dispersion lemmas and conservation laws for some linear kinetic
and quantum-kinetic problems. Comm.
Appl. Nonlinear Anal. 10 (2003), 1--20.
- [108] G. Toscani,
Entropy methods for the asymptotic behaviour of
fourth-order nonlinear diffusion equations. "WASCOM 2001"-11th Conference
on Waves and Stability in Continuous Media (Porto Ercole,
june 3-9, 2001 ), World Sci. Publishing, River Edge, NJ, (2002)
569--578.
- [109] L. Pareschi,
G. Toscani, C. Villani,
Spectral methods for the non cut-off Boltzmann equation and numerical
grazing collision limit, Numer. Math., 93 (2003) 527-548
- [110] A.V. Bobylev,
C. Cercignani, G. Toscani,
Proof of an asymptotic property of self-similar solutions of the Boltzmann
equation for granular materials, J. Statist. Phys., 111 (2003) 403-417
- [111] M.P. Gualdani,
A. Jüngel, G. Toscani,
Exponential decay in time of solutions of the viscous quantum hydrodynamic
equations, Appl. Math. Letters, 16
(2003) 1273-1278
- [112] L. Gosse, G. Toscani, Asymptotic preserving and well-balanced
schemes for radiative transfer and the Rosseland approximation, Numer. Math. 98 ( 2) (2004) 223 - 250
- [113] M. Bisi,
G. Spiga, G. Toscani,
Hydrodynamics from grad's equations for weakly inelastic granular flows,
Physics of Fluids 16 (12) (2004) 4235-4247
- [114] Hailiang
Li, G. Toscani, Long-time asymptotics
of kinetic models of granular flows, Arch. Ration.
Mech. Anal., 172 (3)
(2004) 407-428
- [115] B. Lods,
G. Toscani, The dissipative linear Boltzmann
equation for hard spheres, J. Statist. Phys.,
117 (3-4) (2004) 635-664
- [116] A. Pulvirenti,
G. Toscani, Probabilistic treatment of some
dissipative kinetic models, in "WASCOM 2003"-12th
Conference on Waves and Stability in Continuous Media, World Sci.
Publishing, River Edge, NJ, ( 2004) 407--420
- [117] G. Toscani
et al. Entropy and equilibria of many
particle systems: an essay on recent research. Monatschefte für Mathematik,
142 (1-2) (2004) 35-43
- [118] L. Pareschi,
G. Toscani, Modelling
and numerical methods for granular gases, in "Modeling and
Computational Methods for Kinetic Equations", P. Degond,
L. Pareschi and G. Russo Eds., Birkhauser, Boston (2004) 259-285
- [119] M. Bisi,
G. Toscani, Self-similar solutions of a
nonlinear friction equation in higher dimensions, Ann. Univ. Ferrara - Sez 7 - Ann. Univ. Ferrara - Sez.
VII - Sc. Mat. Vol. L, (2004) 91-110.
- [120] J.A. Carrillo, M.P. Gualdani, G. Toscani,
Finite speed of propagation in porous media by mass transportation
methods, CRAS Série I, 338 (10)
(2004) 815-818
- [121] A. Pulvirenti,
G. Toscani, Asymptotic properties of the
inelastic Kac model, J. Statist. Phys., 114 (2004) 1453-1480
- [122] J.A. Carrillo, G. Toscani, Wasserstein metric and large-time asymptotics of nonlinear diffusion equations, in
New trends in mathematical physics, World Sci. Publ., Hackensack, NJ, (2004) 234–244.
- [123] G. Spiga,
G. Toscani, The dissipative linear Boltzmann
equation. Appl. Math. Letters, 17 (3): 295-301 (2004)
- [124] L. Pareschi,
G.Russo, G. Toscani, A
kinetic approximation of Hele-Shaw flow, CRAS Série I, 338 (2) (2004) 177-182
- [125] G. Toscani,
Kinetic and hydrodinamic models of nearly
elastic granular flows, Monatschefte für Mathematik, 142
(1-2) (2004) 179-192