Roberto Natalini

Elenco delle principali pubblicazioni scientifiche/List of main scientific publications

Updated: November 10, 2018


  1. E. Di Costanzo, M. Menci, E. Messina, R. Natalini, A. Vecchio, A hybrid mathematical model of collective motion under alignment and chemotaxis, arXiv:1507.02980

  2. Gabriella Bretti, Luigi Campanella, Maurizio Ceseri, Roberto Natalini, Filippo Notarnicola, Rita Reale, Maria Pia Sammartino, Giovanni Visco, A Mathematical Model of Iron Rings Formation in Porous Stones, arXiv:1810.11825

  3. Manon Deville, Roberto Natalini, Daniele Peri, Clair Poignard, Emanuela Signori, in preparation.


    1. Manon Deville; Roberto Natalini; Clair Poignard, A continuum mechanics model of enzyme-based tissue degradation in cancer therapies, in Bulletin of Mathematical Biology, online first, October 5th, 2018, (a preliminary version can be found here:

    2. R. Bianchini, R. Natalini, The paradifferential approach to the local well-posedness of some problems in mixture theory in two space dimensions, Communications in Partial Differential Equations (online first November 2018), DOI: 10.1080/03605302.2018.1499775 (a preliminary version can be found here:

    3. Elena Bonetti, Cecilia Cavaterra, Francesco Freddi, Maurizio Grasselli, Roberto Natalini, A nonlinear model for marble sulphation including surface rugosity: theoretical and numerical results, Communications on Pure & Applied Analysis 2019, 18(2): 977-998 doi:10.3934/cpaa.2019048 (a preliminary version can be found here: arXiv:1710.01225)

    4. Roberta Bianchini, Roberto Natalini, Convergence of a vector-BGK approximation for the incompressible Navier-Stokes equations, Kinet. Relat. Models, 12(1) (2019), 133-158. doi: 10.3934/krm.2019006

    5. Francois Bouchut, Yann Jobic, Roberto Natalini, René Occelli, Vincent Pavan, Second-order entropy satisfying BGK-FVS schemes for incompressible Navier-Stokes equations, SMAI-Journal of computational mathematics, 4 (2018), 1-56.

    6. Gabriella Bretti, Roberto Natalini, On modeling Maze solving ability of slime mold via a hyperbolic model of chemotaxis, J. Comput. Methods Sci. Eng. 18, no. 1, (2018), 85-115, 2018, DOI:10.3233/JCM-170773

    7. Ezio Di Costanzo, Alessandro Giacomello, Elisa Messina, Roberto Natalini, Giuseppe Pontrelli, Fabrizio Rossi, Robert Smits, Monika Twarogowska, A discrete in continuous mathematical model of cardiac progenitor cells formation and growth as spheroid clusters (Cardiospheres), Mathematical Medicine And Biology: A Journal of the Ima, 35 (2018), 121-144, Published online on January 2017 . doi:

    8. A. L. Amadori, R. Natalini, D. Palmigiani, A rare mutation model in heterogeneous environment with simulations for the hawk and dove game, Ecological Complexity, 34, (2018), 188-197. doi:

    9. Roberta Bianchini, Roberto Natalini, Well-posedness of a model of nonhomogeneous compressible-incompressible fluids, J. Hyperbolic Differ. Equ. 14 (2017), no. 3, 487-516. doi:

    10. M.P. Bracciale, G. Bretti, A. Broggi, M. Ceseri, A. Marrocchi, R. Natalini, C. Russo, Crystallization Inhibitors: Explaining Experimental Data through Mathematical Models. Applied Mathematical Modelling, Volume 48, August 2017, Pages 21-38. doi:

    11. M. Leguèbe, R. Natalini, M.G. Notarangelo, C. Poignard, M. Twarogowska, Mathematical model for transport of DNA plasmids from the external medium up to the nucleus by electroporation, Math. Biosci. Volume 285, March 2017, Pages 1-13. doi:

    12. Di Costanzo E, Ingangi V, Angelini C, Carfora MF, Carriero MV, Natalini R, A Macroscopic Mathematical Model for Cell Migration Assays Using a Real-Time Cell Analysis.PLoS ONE 11(9) (2016): e0162553. doi:10.1371/journal.pone.0162553

    13. Fabrizio Clarelli, Cristiana Di Russo, Roberto Natalini, Magali Ribot, A fluid dynamics multidimensional model of biofilm growth: stability, influence of environment and sensitivity, Mathematical Medicine and Biology, Volume 33, Issue 4, 1 December 2016, Pages 371–395,

    14. Denise Aregba-Driollet, Maya Briani, and Roberto Natalini, Time Asymptotic High Order Schemes for Dissipative BGK Hyperbolic Systems. Numer. Math. (2016) 132:399-431, DOI 10.1007/s00211-015-0720-y

    15. A. L. Amadori, M. Briani, R. Natalini, A non-local rare mutations model for quasispecies and prisoner's dilemma: Numerical assessment of qualitative behaviour. European J. Appl. Math. 27 (2016), no. 1, 87—110. DOI: 10.1017/S0956792515000352.

    16. R. Bianchini, R. Natalini, Global existence and asymptotic stability of smooth solutions to a fluid dynamics model of biofilms in one space dimension, Journal of Mathematical Analysis and Applications, 434 (2) (2016) , 1909-1923.

    17. F.R. Guarguaglini, R. Natalini, Global smooth solutions for a hyperbolic chemotaxis model on a network, SIAM J. Math. Anal. 47-6 (2015), 4652-4671.

    18. Anna Lisa Amadori, Antonella Calzolari, Roberto Natalini, Barbara Torti, Rare mutations in evolutionary dynamics, Journal of Differential Equations, 259 (11), 6191-6214.

    19. R. Natalini, M. Ribot, M. Twarogowska; A numerical comparison between degenerate parabolic and quasilinear hyperbolic models of cell movements under chemotaxis. Journal of Scientific Computing, Volume 63 (3) (2015), 654-677. DOI: 10.1007/s10915-014-9909-y

    20. E. Di Costanzo, R. Natalini, L. Preziosi, A hybrid mathematical model for self-organizing cell migration in the zebrafish lateral line, J. Math. Bio. Volume 71, Issue 1 (2015), 171-214. DOI: 10.1007/s00285-014-0812-9

    21. G. Alì, R. Natalini, I. Torcicollo, Global existence for a 1D parabolic-elliptic model for chemical aggression in permeable materials, Nonlinear Analysis: Real World Applications, Volume 21 (2015), 1–12, DOI: 10.1016/j.nonrwa.2014.05.006.

    22. Notarangelo M. G., Natalini R., Signori E., Gene therapy: the role of cytoskeleton in gene transfer studies based on biology and mathematics. Curr Gene Ther. (2014) ;14(2) :121-7.

    23. Clarelli, F.; De Filippo, B.; Natalini, R., A mathematical model of copper corrosion, Appl. Math. Mod. Volume: 38 (2014) 4804-4816.

    24. J. Elias, L. Dimitrio, J. Clairambault, R. Natalini, Dynamics of p53 in single cells: physiologically based ODE and reaction-diffusion PDE models, Phys. Biol. 11  (2014), 045001. doi:10.1088/1478-3975/11/4/045001

    25. Ján Elias; Luna Dimitrio; Jean Clairambault; Roberto Natalini, The p53 protein and its molecular network: modelling a missing link between DNA damage and cell fate, Biochimica et Biophysica Acta - Proteins and Proteomics, Volume:1844, Issue: 1, Special Issue: SI, Pages: 232-247, Part: B, (2014).

    26. G. Bretti, R. Natalini, M. Ribot, A hyperbolic model of chemotaxis on a network: a numerical study, ESAIM: Mathematical Modelling and Numerical Analysis, Volume: 48, Issue: 1, Pages: 231-25, DOI:10.1051/m2an/2013098.

    27. R. Natalini, M. Ribot, M. Twarogowska.; A well-balanced numerical scheme for a one dimensional quasilinear hyperbolic model of chemotaxis, Comm. Math. Sci. 12 (2014), 13-29.

    28. M. Briani, G. Germani, E. Iannone. M. Moroni, R. Natalini; Design and Optimization of Reaction Chamber and Detection System in Dynamic Labs-on-Chip for Proteins Detection, IEEE Transactions on Biomedical Engineering, 60 (2013), 2161–2166.

    29. Luna Dimitrio, Jean Clairambault, Roberto Natalini; A spatial physiological model for p53 intracellular dynamics, J. Theor. Bio. v. 316, (2013), 9–24.

    30. F. Clarelli, C. Di Russo, R. Natalini and M. Ribot, A fluid dynamics model of the growth of phototrophic biofilms, J. Math. Biol. 66 (2013), no. 7, 1387—1408.

    31. R. Natalini, M. Ribot. Asymptotic High Order Mass-Preserving Schemes for a Hyperbolic Model of Chemotaxis, SIAM Journal on Numerical Analysis 50 (2012), pp. 883-905.

    32. A. Amadori, B. Boccabella, R. Natalini. A hyperbolic model of spatial evolutionary game theory. Comm. Pure Appl. Analysis 11, (2012), 981 – 1002. doi: 10.3934/cpaa.2012.11.981

    33. Boccabella, Astridh; Natalini, Roberto; Pareschi, Lorenzo. On a continuous mixed strategies model for evolutionary game theory. Kinet. Relat. Models 4 (2011), no. 1, 187--213.

    34. A. Cangiani, R. Natalini, A spatial model of cellular molecular trafficking including active transport along microtubules. Journal of Theoretical Biology, 267; (2010) p. 614-625, ISSN: 0022-5193, doi: 10.1016/j.jtbi.2010.08.017.

    35. F. Clarelli, R. Natalini, A pressure model of immune response to mycobacterium tuberculosis infection in several space dimensions, Mathematical Biosciences and Engineering, Volume: 7 Issue: 2 Pages: 277-300 Published: APR 2010

    36. Anna Lisa Amadori, Astridh Boccabella, Roberto Natalini, A One Dimensional Hyperbolic Model for Evolutionary Game Theory: Numerical Approximations and Simulations, Communications in Applied and Industrial Mathematics, 1, 1, (2010) 1–21.

    37. Cristiana Di Russo, Roberto Natalini, Magali Ribot, Global existence of smooth solutions to a two-dimensional hyperbolic model of chemotaxis, Communications in Applied and Industrial Mathematics, 1, 1, (2010) 92–109.

    38. C. Mascia, R. Natalini, On Relaxation Hyperbolic Systems violating the Shizuta--Kawashima condition, Archive for Rational Mechanics and Analysis, Volume 195, Number 3 / March, 2010, DOI 10.1007/s00205-009-0225-x, Pages 729-762.

    39. F. Guarguaglini, C. Mascia, R. Natalini, M. Ribot, Global stability of constant states and qualitative behavior of solutions to a one dimensional hyperbolic model of chemotaxis, Discrete and Continuous Dynamical Systems - Series B, 12, 2009, 39-76.

    40. Davide Vergni, Filippo Castiglione, Maya Briani, Silvia Middei, Elena Alberdi, Klaus G. Reymann, Roberto Natalini, Cinzia Volonté, Carlos Matute, Fabio Cavaliere, A Model of Ischemia-Induced Neuroblast Activation in the Adult Subventricular Zone, PLoS ONE, 4 (4) 2009, art. no. e5278.

    41. Carbou, G.; Hanouzet, B.; Natalini, R. Semilinear behavior for totally linearly degenerate hyperbolic systems with relaxation. J. Differential Equations 246 (2009), no. 1, 291–319.

    42. Aregba-Driollet, Denise; Bretti, Gabriella; Natalini, Roberto. Numerical schemes for the Barenblatt model of non-equilibrium two-phase flow in porous media.Quart. Appl. Math. 66 (2008), no. 2, 201–231.

    43. Carfora, Maria Francesca; Natalini, Roberto A discrete kinetic approximation for the incompressible Navier-Stokes equations. M2AN Math. Model. Numer. Anal. 42 (2008), no. 1, 93–112.

    44. Clarelli, Fabrizio; Fasano, Antonio; Natalini, Roberto Mathematics and monument conservation: free boundary models of marble sulfation. SIAM J. Appl. Math. 69 (2008), no. 1, 149–168.

    45. Giavarini C, Santarelli ML, Natalini R., Freddi F (2008). A non- linear model of sulphation of porous stones: Numerical simulations and preliminary laboratory assessments. Journal of Cultural Heritage, vol. 9; p. 14-22, ISSN: 1296-2074.

    46. Aregba-Driollet, Denise; Briani, Maya; Natalini, Roberto Asymptotic high-order schemes for 2×2 dissipative hyperbolic systems. SIAM J. Numer. Anal. 46 (2008), no. 2, 869–894.

    47. Bianchini, Stefano; Hanouzet, Bernard; Natalini, Roberto Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy. Comm. Pure Appl. Math. 60 (2007), no. 11, 1559–1622.

    48. G. Bretti, R. Natalini, B. Piccoli, A Fluid-Dynamic Traffic Model on Road Networks, Archives of Computational Methods in Engineering 14 (2007), 139-172; available at springerlink.

    49. M. Briani, R. Natalini, G. Russo, Implicit-Explicit Numerical Schemes for Jump--Diffusion Processes; Calcolo 44 (2007), 33-57.

    50. F. R. Guarguaglini and R. Natalini, Fast reaction limit and large time behavior of solutions to a nonlinear model of sulphation phenomena, Commun. Partial Differ. Equations 32 (2007), 163-189.

    51. F.R. Guarguaglini, R. Natalini Nonlinear transmission problems for quasilinear parabolic systems, Networks and Heterogeneous Media 2, n.2 (2007), 359- 381.

    52. F. R. Guarguaglini, R. Natalini, Global existence and uniqueness of solutions for multidimensional weakly parabolic systems arising in chemistry and biology, (CPAA) Volume 6, Number: 1 (2007), 287-309.

    53. M. Garavello, R. Natalini, B. Piccoli and A. Terracina, Conservation laws with discontinuous, Networks and Heterogeneous Media 2, n.1 (2007), 159 – 179.

    54. G. Alì, V. Furuholt, R. Natalini, and I. Torcicollo, A mathematical model of sulphite chemical aggression of limestones with high permeability. Part I. Modeling and qualitative analysis, Transport in Porous Media, Volume 69, Number 1 (2007), 109-122.

    55. G. Alì, V. Furuholt, R. Natalini, and I. Torcicollo, A mathematical model of sulphite chemical aggression of limestones with high permeability. Part II: Numerical approximation, Transport in Porous Media, Volume 69, Number 2 (2007), 175-188.

    56. Briani, Maya; Natalini, Roberto. Asymptotic high-order schemes for integro-differential problems arising in markets with jumps. Commun. Math. Sci. 4 (2006), no. 1, 81-96.

    57. Natalini, R.; Rousset, F. Convergence of a singular Euler-Poisson approximation of the incompressible Navier-Stokes equations. Proc. Am. Math. Soc. 134, No.8, 2251-2258 (2006).

    58. G. Bretti, R. Natalini, B. Piccoli, Numerical Approximations of a Traffic Flow Model on Networks, Networks and Heterogeneous Media 1, No.1, 57-84 (2006).

    59. Bretti, Gabriella; Natalini, Roberto; Piccoli, Benedetto. Fast algorithms for the approximation of a traffic flow model on networks. Discrete Contin. Dyn. Syst. Ser. B 6 (2006), no. 3, 427—448.

    60. F. R. Guarguaglini and R. Natalini, Global existence of solutions to a nonlinear model of sulphation phenomena in calcium carbonate stones, Nonlinear Analysis: Real World Applications, Volume 6, Issue 3 (2005), Pages 477-494.

    61. D. Aregba-Driollet, F. Diele, and R. Natalini. A Mathematical Model for the SO2 Aggression to Calcium Carbonate Stones: Numerical Approximation and Asymptotic Analysis, SIAM J. APPL. MATH. (2004) 64, No. 5, pp. 1636 1667.

    62. M. Briani, C. La Chioma, R. Natalini Convergence of numerical schemes for viscosity solutions to integro-differential degenerate parabolic problems arising in financial theory, Numer. Math. 98 (2004), no. 4, 607—646.

    63. Y. Brenier, R. Natalini, and M. Puel On a relaxation approximation of the incompressible Navier-Stokes equations; Proc. Am. Math. Soc. 132, No.4, 1021-1028 (2004).

    64. D. Aregba-Driollet, R. Natalini, S.Q. Tang , Diffusive kinetic explicit schemes for nonlinear degenerate parabolic systems, Math. Comp. 73 (2004) 63-94.

    65. B. Hanouzet, R. Natalini. Global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy, Arch. Ration. Mech. Anal. 169 (2003), 89-117.

    66. R. Natalini, C. Nitsch, G. Pontrelli, S. Sbaraglia. A numerical study of a nonlocal model of damage propagation under chemical aggression, European Journal of Applied Mathematics Volume 14, Issue 4, (2003) p. 447-464.

    67. A. L. Amadori, R. Natalini, Entropy solutions to a strongly degenerate anisotropic convection-diffusion equation, with application to the backward-forward stochastic differential utility, J. Math. Anal. Appl. 284/2 (2003), 511-531.

    68. Lattanzio, Corrado; Natalini, Roberto. Convergence of diffusive BGK approximations for nonlinear strongly parabolic systems. Proc. Roy. Soc. Edinburgh Sect. A 132 (2002), no. 2, 341--358.

    69. Natalini, Roberto; Terracina, Andrea. Convergence of a relaxation approximation to a boundary value problem for conservation laws. Comm. Partial Differential Equations 26 (2001), no. 7-8, 1235--1252.

    70. H. Liu and and R. Natalini, Long-Time Diffusive Behavior of Solutions to a Hyperbolic Relaxation System, Asymptot. Anal. 25 (2001), no. 1, 21--38.

    71. F. Bouchut, F.R. Guarguaglini and R. Natalini, Diffusive BGK Approximations for Nonlinear Multidimensional Parabolic Equations, Indiana Univ. Math. J. 49 (2000), 723-749.

    72. R. Natalini and S. Tang, Discrete Kinetic Models for Dynamical Phase Transitions, Commun. Appl. Nonlinear Anal. 7 (2000), 12-32.

    73. Denise Aregba-Driollet and Roberto Natalini, Discrete Kinetic Schemes for Multidimensional Conservation Laws, SIAM J. Num. Anal. 37 (2000), 1973-2004.

    74. Gilding, Brian H.; Natalini, Roberto; Tesei, Alberto, How parabolic free boundaries approximate hyperbolic fronts. Trans. Amer. Math. Soc. 352 (2000), no. 4, 1797--1824.

    75. Tao Luo, Roberto Natalini and Tong Yang, Global BV solutions to a p-system with relaxation, Quaderno IAC 12/1998; J. Differential Equations 162 (2000), no. 1, 174--198.

    76. Roberto Natalini and Alberto Tesei, On the Barenblatt Model for Non-Equilibrium Two Phase Flow in Porous Media, Arch. Ration. Mech. Anal. 150 (1999), no. 4, 349--367.

    77. Gasser, Ingenuin; Natalini, Roberto The energy transport and the drift diffusion equations as relaxation limits of the hydrodynamic model for semiconductors. Quart. Appl. Math. 57 (1999), no. 2, 269–282.

    78. LeFloch, Philippe G.; Natalini, Roberto Conservation laws with vanishing nonlinear diffusion and dispersion. Nonlinear Anal. 36 (1999), no. 2, Ser. A: Theory Methods, 213--230.

    79. Brenier, Yann; Corrias, Lucilla; Natalini, Roberto, Relaxation limits for a class of balance laws with kinetic formulation. Advances in nonlinear partial differential equations and related areas (Beijing, 1997), 2--14, World Sci. Publishing, River Edge, NJ, 1998.

    80. Luo, Tao; Natalini, Roberto; Xin, Zhouping Large time behavior of the solutions to a hydrodynamic model for semiconductors. SIAM J. Appl. Math. 59 (1998), no. 3, 810—830.

    81. Luo, Tao; Natalini, Roberto BV solutions and relaxation limit for a model in viscoelasticity. Proc. Roy. Soc. Edinburgh Sect. A 128 (1998), no. 4, 775--795.

    82. Natalini, Roberto A discrete kinetic approximation of entropy solutions to multidimensional scalar conservation laws. J. Differential Equations 148 (1998), no. 2, 292--317.

    83. Hanouzet, Bernard; Natalini, Roberto; Tesei, Alberto On the Chapman-Jouguet limit for a combustion model. SIAM J. Math. Anal. 29 (1998), no. 3, 619--636.

    84. Marcati, Pierangelo; Natalini, Roberto Global weak entropy solutions to quasilinear wave equations of Klein-Gordon and sine-Gordon type. J. Math. Soc. Japan 50 (1998), no. 2, 433--449.

    85. Natalini, R.; Sinestrari, C.; Tesei, A. Incomplete blowup of solutions of quasilinear hyperbolic balance laws. Arch. Rational Mech. Anal. 135 (1996), no. 3, 259--296.

    86. Mascia, Corrado; Natalini, Roberto $L\sp 1$ nonlinear stability of traveling waves for a hyperbolic system with relaxation. J. Differential Equations 132 (1996), no. 2, 275--292.

    87. Natalini, Roberto; Hanouzet, Bernard Weakly coupled systems of quasilinear hyperbolic equations. Differential Integral Equations 9 (1996), no. 6, 1279--1292.

    88. Aregba-Driollet, Denise; Natalini, Roberto Convergence of relaxation schemes for conservation laws. Appl. Anal. 61 (1996), no. 1-2, 163--193.

    89. Natalini, Roberto Convergence to equilibrium for the relaxation approximations of conservation laws. Comm. Pure Appl. Math. 49 (1996), no. 8, 795--823.

    90. Natalini, Roberto; Rubino, Bruno A discrete approximation for hyperbolic systems with quadratic interaction term. Comm. Appl. Nonlinear Anal. 3 (1996), no. 2, 1--21.

    91. Natalini, R. The bipolar hydrodynamic model for semiconductors and the drift-diffusion equations. J. Math. Anal. Appl. 198 (1996), no. 1, 262--281.

    92. Kersner, R.; Natalini, R.; Tesei, A. Shocks and free boundaries: the local behaviour. Asymptotic Anal. 10 (1995), no. 1, 77--93.

    93. Marcati, Pierangelo; Natalini, Roberto Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation. Arch. Rational Mech. Anal. 129 (1995), no. 2, 129--145.

    94. Corrias, L.; Falcone, M.; Natalini, R. Numerical schemes for conservation laws via Hamilton-Jacobi equations. Math. Comp. 64 (1995), no. 210, 555--580.

    95. Marcati, Pierangelo; Natalini, Roberto Weak solutions to a hydrodynamic model for semiconductors: the Cauchy problem. Proc. Roy. Soc. Edinburgh Sect. A 125 (1995), no. 1, 115--131.

    96. Claudi, S.; Natalini, R.; Tesei, A. Large time behaviour of a diffusion equation with strong convection. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 21 (1994), no. 3, 445--474.

    97. Marcati, Pierangelo; Natalini, Roberto Convergence of the pseudo-viscosity approximation for conservation laws. Nonlinear Anal. 23 (1994), no. 5, 621--628.

    98. Natalini, R.; Tesei, A. Blow-up of solutions for a class of balance laws. Comm. Partial Differential Equations 19 (1994), no. 3-4, 417--453).

    99. Natalini, Roberto; Tesei, Alberto Blow-up of solutions of first order quasilinear hyperbolic equations. Appl. Anal. 51 (1993), no. 1-4, 81--114.

    100. Natalini, R. Unbounded solutions for conservation laws with source. Nonlinear Anal. 21 (1993), no. 5, 349--362.

    101. Natalini, R.; Tesei, A. On a class of perturbed conservation laws. Adv. in Appl. Math. 13 (1992), no. 4, 429--453.

    102. Arosio, Alberto; Natalini, Roberto; Paoli, Maria Gabriella. Fourth order quasilinear evolution equations of hyperbolic type. J. Math. Soc. Japan 44 (1992), no. 4, 619--630.

    103. Natalini, Roberto Multiplication de distributions avec conditions de compatibilité. Ann. Fac. Sci. Toulouse Math. (5) 10 (1989), no. 1, 75--91.

    Books (author and editor)

    1. Roberto Natalini, Anna Baccaglini-Frank, Pietro Di Martino, Giuseppe Rosolini, Didattica della Matematica, Mondadori Università, 2018, ISBN: 9788861845503.

    2. Gosse, Laurent, Natalini, Roberto (Eds.), Innovative Algorithms and Analysis, Springer INdAM Series, Series Volume 16, 2017, Springer International Publishing, eBook ISBN 978-3-319-49262-9, DOI: 10.1007/978-3-319-49262-9, Hardcover ISBN 978-3-319-49261-2, Series ISSN, 2281-518X, Number of Pages XVIII, 351

    3. P A Marcati, P A Markowich, Roberto Natalini (Eds.), Mathematical Problems in Semiconductor Physics, December 15, 1995 by Chapman and Hall/CRC, 224 Pages ISBN 9780582287044 - CAT# LM8704 Series: Chapman & Hall/CRC Research Notes in Mathematics Series

    Lecture Notes

    1. R. Natalini, Introduzione ai metodi numerici alle differenze finite per equazioni di evoluzione, Appunti del corso tenuto nel quadro della XVIII SCUOLA DI MATEMATICA COMPUTAZIONALE organizzata dall'Istituto per le Applicazioni della Matematica di Napoli, Vico Equense, 11-16 Settembre 2000. (In Italian);

    2. Natalini, Roberto Recent results on hyperbolic relaxation problems. Analysis of systems of conservation laws (Aachen, 1997), 128--198, Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math., 99, Chapman & Hall/CRC, Boca Raton, FL, 1999. 35L65 (35B35 76N15);

    Some proceedings e short refereed papers

    1. Alessandro Corbetta, Caterina Balzotti, Maya Briani, Emiliano Cristiani, Marina Minozzi, Roberto Natalini, Sara Suriano, Federico Toschi. Forecasting visitors' behaviour in crowded museums - a case study: the Galleria Borghese in Rome, Poster for the Conference: Pedestrian and Evacuation Dynamics 18, August 2018, DOI: 10.13140/RG.2.2.28540.18567

    2. De Filippo. B, Natalini R., Copper corrosion: A mathematical model for the simulation of chemical processes, Metallurgia Italiana, 109(7-8), 2017, 71-74.

    3. Dimitrio, L., Natalini, R., Milanesi, L., A mathematical model for the enhanced cytoplasmic transport: How to get (faster) to the nucleus (2011) BIOINFORMATICS 2011 - Proceedings of the International Conference on Bioinformatics Models, Methods and Algorithms, pp. 39-46.

    4. Bretti, Gabriella; Natalini, Roberto; Ribot, Magali, A Numerical Scheme for a Hyperbolic Relaxation Model on Networks, AIP Conference Proceedings Volume: 1389 DOI: 10.1063/1.3637886 Published: 2011.

    5. Clarelli, F.; Di Russo, C.; Natalini, R.; Ribot, M. Mathematical models for biofilms on the surface of monuments. Applied and industrial mathematics in Italy III, 220–231, Ser. Adv. Math. Appl. Sci., 82, World Sci. Publ., Hackensack, NJ, 2010.

    6. Clarelli, Fabrizio; Natalini, Roberto; Nitsch, Carlo; et al., A Mathematical Model for Consolidation of Building Stones, Series on Advances in Mathematics for Applied Sciences Volume: 82 Pages: 232-243 DOI: 10.1142/9789814280303_0021 Published: 2010.

    7. R. Natalini, C. Nitsch, F. Freddi, Mathematical models for damage monitoring and restoration of cultural heritage, in"Proceedings of the JSIAM-SIMAI meeting 2005", GAKUTO International Series, Mathematical Sciences and Applications 2008. (2008), 14-22.

    8. F. Clarelli, C.Giavarini, R.Natalini, C. Nitsch, M.L.Santarelli, Mathematical models for the consolidation processes in stones, to appear in Eds. J. Delgado Rodrigues, Proc. of "International Symposium: Stone Consolidation in Cultural Heritage - research and practice", Lisbona May 2008.

    9. Aregba-Driollet, Denise; Briani, Maya; Natalini, Roberto. AHO schemes for dissipative hyperbolic systems. CANUM 2006—Congrès National d'Analyse Numérique, 52--66, ESAIM Proc., 22, EDP Sci., Les Ulis, 2008.

    10. Garavello, M., Natalini, R., Piccoli, B.; Terracina, A. A Riemann solver approach for conservation laws with discontinuous flux. Hyperbolic problems: theory, numerics, applications, 1029–1036, Springer, Berlin, 2008.

    11. Bianchini, S.; Hanouzet, B.; Natalini, R. Dissipative hyperbolic systems: the asymptotic behavior of solutions. Hyperbolic problems: theory, numerics, applications, 59–73, Springer, Berlin, 2008.

    12. Bretti, G.; Natalini, R.; Piccoli, B., Numerical algorithms for simulations of a traffic model on road networks, Journal of Computational and Applied Mathematics, Volume: 210 Issue: 1-2 Pages: 71-77 DOI: 10.1016/ Published: DEC 31 2007.

    13. L. Appolonia, E. Borrelli, R. Natalini, M.L.Santarelli. “Determinazione dell'evoluzione delle croste in gesso mediante un modello matematico: analisi numerica e risultati sperimentali” in LO STATO DELL'ARTE, Conservazione e restauro. Confronto di esperienze, Atti del II Congresso Nazionale IGIIC, Palazzo Reale, Genova 27/29 Settembre 2004.

    14. E. Borrelli, C. Giavarini, M. Incitti, R. Natalini, M.L. Santarelli, "Material model for the evolution of gypsum crusts: numerical and experimental results" in Proceedings of "Stone2004", June 2004, Stockholm, Sweden.

    15. Aregba-Driollet, D; Natalini, R; Tang, SQ, Diffusive discrete BGK schemes for nonlinear hyperbolic-parabolic systems, Hyperbolic Problems: Theory, Numerics, Applications, Hyperbolic Problems: Theory, Numerics, Applications, Vols I and II Book Series: International Series of Numerical Mathematics Volume: 140 Pages: 49-58 Published: 2001.

    16. Natalini, R; Tang, SQ, Discrete BGK models for dynamic phase transitions in one-dimension, Hyperbolic Problems: Theory, Numerics, Applications, Vols I and II Book Series: International Series of Numerical Mathematics Volume: 140 Pages: 765-774 Published: 2001.

    17. Aregba-Driollet, D; Natalini, R, Discrete kinetic schemes for systems of conservation laws, Hyperbolic Problems: Theory, Numerics, Applications, Vol 1 Book Series: International Series of Numerical Mathematics, Volume: 129 Pages: 1-10 Published: 1999.

    18. Gilding, Brian H.; Natalini, Roberto; Tesei, Alberto How parabolic free boundaries approximate hyperbolic fronts. International Symposium on Differential Equations and Mathematical Physics (Tbilisi, 1997). Mem. Differential Equations Math. Phys. 12 (1997), 62–67.

    19. Hanouzet, B.; Natalini, R. Systems of quasilinear hyperbolic equations with quadratic coupling. Nonlinear evolutionary partial differential equations (Beijing, 1993), 509–513, AMS/IP Stud. Adv. Math., 3, Amer. Math. Soc., Providence, RI, 1997.

    20. Marcati, P. A.; Natalini, R. Entropy solutions for a hydrodynamic model for semiconductors. Nonlinear evolutionary partial differential equations (Beijing, 1993), 311–317, AMS/IP Stud. Adv. Math., 3, Amer. Math. Soc., Providence, RI, 1997.

    21. Marcati, P. A.; Natalini, R. On the hydrodynamic model for semiconductors and the relaxation to the drift-diffusion equation. Hyperbolic problems: theory, numerics, applications (Stony Brook, NY, 1994), 198–206, World Sci. Publ., River Edge, NJ, 1996.

    22. Ali, G; Marcati, PA; Natalini, R, Hydrodynamical models for semiconductors, Zeithschrift fur Angewandte Mathematik und Mechanik, Volume: 76 Supplement: 2 Pages: 301-304 Published: 1996.

    23. Aregba Driollet, D; Natalini, R, Convergence of relaxation schemes for conservation laws, Zeithschrift fur Angewandte Mathematik und Mechanik, Volume: 76 Supplement: 2 Pages: 377-380 Published: 1996.

    24. Natalini, R, Uniform convergence to equilibrium for conservation laws with relaxation, Zeithschrift fur Angewandte Mathematik und Mechanik, Volume: 76 Supplement: 2 Pages: 385-388 Published: 1996.

    25. Marcati, P. A.; Natalini, R. Relaxation phenomena for the hydrodynamic models in semiconductors. Mathematical problems in semiconductor physics (Rome, 1993), 153–164, Pitman Res. Notes Math. Ser., 340, Longman, Harlow, 1995.

    26. Corrias, L.; Falcone, M.; Natalini, R. On a class of large time-step schemes for conservation laws. Nonlinear hyperbolic problems: theoretical, applied, and computational aspects (Taormina, 1992), 159–170, Notes Numer. Fluid Mech., 43, Friedr. Vieweg, Braunschweig, 1993.

    27. Arosio, A.; Natalini, R.; Panizzi, S.; Paoli, M. G. Fourth order evolution equations. International Conference on Differential Equations, Vol. 1, 2 (Barcelona, 1991), 282–287, World Sci. Publ., River Edge, NJ, 1993.

    28. Arosio, A.; Natalini, R.; Panizzi, S.; Paoli, M. G. Fourth order abstract evolution equations. Nonlinear hyperbolic equations and field theory (Lake Como, 1990), 8–22, Pitman Res. Notes Math. Ser., 253, Longman Sci. Tech., Harlow, 1992.

    29. Natalini, Roberto Solutions non bornées pour des lois de conservation avec source. (French) [Unbounded solutions for conservation laws with source] C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), no. 11, 731–734.

    30. Natalini, Roberto Formules de produit pour des distributions à valeurs dans C^N. (French) [Product formulas for C^N-valued distributions] C. R. Acad. Sci. Paris Sér. I Math. 302 (1986), no. 19, 685–688.

    Printed papers about Outreach in Mathematics (mainly in Italian).

    1. Roberto Natalini, "La Matematica - solo quella applicata?- non è più quella di una volta" (Mathematics, only applied mathematics?, is no more as before), Lettera Matematica Pristem 49, december 2003.

    2. Roberto Natalini, “Prevedere le ingiurie del tempo" (Forecast the damage), Sapere, august 2004.

    3. Interview by Roberto Natalini and Maurizio Mattaliano, “La fantasia e la memoria: intervista a Emma Castelnuovo” (The imagination and the memory: an interview to Emma Castelnuovo), Lettera matematica Pristem 51, august 2004.

    4. Roberto Natalini, “Il fratello maggiore di FINAC” (The FINAC's big brother), Lettera matematica Pristem 55, july 2005

    5. Interview by Rosella Panarese and Roberto Natalini, "Intervista a Andrew Wiles" (Interview to Andrew Wiles), Lettera matematica Pristem 56, october 2005

    6. Roberto Natalini, "Indagine su un fisico al di sopra di ogni sospetto" (Investigation of a Physicist Above Suspicion), Lettera matematica Pristem 59, june 2006.

    7. Antonio Fasano and Roberto Natalini, “Lost Beauties of the Acropolis: What Mathematics Can Say”, SIAM News Volume 39, Number 6, July/August 2006. EN Transalated in Italian: Antonio Fasano and Roberto Natalini, "La Matematica per i beni culturali: le bellezze perdute dell'Acropoli" (Mathematics for cultural heritage: the lost beauties of the Acropoli), Lettera matematica Pristem 60, october 2006.

    8. Roberto Natalini, "CNR: novità non ce ne sono" (No news from the CNR), Lettera matematica Pristem 60, october 2006.

    9. Roberto Natalini, “Equazioni differenziali alle derivate parziali” (Partial differential equations), Enciclopedia Italiana Treccani, VII Appendice (2006).

    10. Michiel Bertsch and Roberto Natalini, "Viaggio all'interno dell'Italia matematica: l'IAC-CNR di Roma” (A travel in the Italian Mathematics: the IAC-CNR in Rome), Lettera matematica Pristem 64, april 2007.

    11. Interview by M. Motta e R. Natalini “Intervista a Peter Lax: 'La Matematica pura? Una branca di quella applicata'” (Interview to Peter Lax: “Pure Math? Just a branch of Applied Math”), Lettera matematica Pristem 65, october 2007.

    12. Roberto Natalini e Francesco Freddi, “Salviamo i monumenti ... con le simulazioni numeriche” (Save the monuments... with numerical simulations), Rivista della Facoltà di Archietettura dell'Università di Parma, october 2008.

    13. Roberto Natalini, “La matematica e il capitalismo” (Math and Capitalism), Newton, february 2010.

    14. Christopher Hauert, Roberto Natalini, “L'unione fa la forza” (Unity is strenght), Newton, september 2010.

    15. Roberto Natalini, Stefano Pisani, Chiara Valerio, "Non capisci la matematica? Allora leggila!" (Do you not understand math? So, read it!), in Atti dell'ottavo Convegno nazionale sulla comunicazione della scienza, N. Pitrelli et al. Eds., Polimetrica 2010, p, 107-114.

    16. Roberto Natalini, “La matematica e la realtà: le sfide del CNR” (Mathematics and Reality: the CNR challenges), in “Nuovi ponti tra scienza e società. Il CNR, crocevia della cultura italiana”, Bollati Boringhieri 2011, p. 47-60.

    17. Roberto Natalini, “L'incidente” (The accident), in AA.VV. “La fine dei dinosauri”, Edizioni Nottetempo, 2011, pp- 67-82.

    18. Roberto Natalini, "Maddmaths : ovvero l'infinita ricerca di un nuovo modo di raccontare la matematica (e non solo quella applicata)" (MaddMaths! or the infinite quest of a new way to tell the math), Archimede, vol. 1 (2012), 19-21.

    19. Roberto Natalini, “Uno scienziato al cinema - The social network” (A scientist goes to the movies: The Social Network), Linx Magazine n.14, january 2013, pp. 60-61.

    20. Roberto Natalini, “David Foster Wallace and the Mathematics of Infinity" in Burn, Stephen, and Boswell, Marshall, eds. “A Companion to David Foster Wallace Studies”. Palgrave Macmillan, 2013 (American Literature Readings in the Twenty-First Century), p. 43-57. EN

    21. Roberto Natalini, "MaddMaths!" (MaddMaths!), Accastampato n. 10, june 2013.

    22. Roberto Natalini, Book Review: “L'Equation du Millénaire” (Book review: The millenium equation) , EMS Newsletter, n. 89, September 2013. p. 58—59. EN

    23. Roberto Natalini, “Consistenza matematica, una storia abbastanza complicata” (Mathematica consistency: a quite complicate story), Liberascienza Magazine, september 2013.

    24. Roberto Natalini, Andrea Plazzi (Eds.), "Comics & Science" (inside the comics story MISTERIUS Speciale Scienza by Leo Ortolani), Edizioni CNR, october 2013.

    25. Roberto Natalini, “Macchie, strisce e rosette: come si formano le forme” (Spots, stripes and rosettas: how the shapes are formed), Sapere , february 2014.

    26. Roberto Natalini, Stefano Pisani, “Matematica Eccellenza” (Mathematical Excellence), Il Sole24ore, august 2014.

    27. Roberto Natalini, Andrea Plazzi (Eds.), "Comics & Science @CERN" (inside the comics story ORAMAI by Tuono Pettinato), Edizioni CNR, october 2014.

    28. Roberto Natalini, Andrea Plazzi (Eds.), “Comics&Science Materia Oscura” (inside the comics story Materia Oscura by Silver and Francesco Artibani and a graphic article by Claudia Flandoli), Edizioni CNR, may 2016.

    29. Roberto Natalini, Andrea Plazzi (Eds.), “Comics&Science, The Internet Issue” (inside the comics stories Misterius, Speciale Internet by Leo Ortolani and Avanti tutta! By Federico Bertolucci), Edizioni CNR, november 2016

    30. Roberto Natalini, Andrea Plazzi (Eds.), “Comics&Science, The Babbage Issue” (inside the comics story Il Segreto di Babbage by Alfredo Castelli and Gabriele Peddes), Edizioni CNR, may 2017.

    31. Roberto Natalini, Raccontare la Matematica: gioie e dolori, in LE PAROLE DELLA SCIENZA, Comunicare nell'era della conoscenza, Pietro Greco Ed., Scienza & Società 29-30, Edizioni Egea, pp. 97-106.

    32. Silvia Benvenuti, Roberto Natalini, Comunicare la matematica: chi, come, dove, quando e soprattutto perché?!, Rivista dell'Unione Matematica Italiana, Serie I, Vol. 2, N. 2, Agosto 2017.

    33. Roberto Natalini, Bringing a new light on old problems - Interview with Laure Saint-Raymond, EMS Newsletter, September 2017, pp. 23–25. EN

    34. Roberto Natalini, Andrea Plazzi (Eds.), “Comics&Science, The Archimedes Issue” (inside the comics story Archimede Infinito 2.0 by Giuseppe Palumbo), Edizioni CNR, November 2017.

    35. Roberto Natalini, More than just numbers, Pan European Networks: Science & Technology 25, December 2017, pp. 66-67

    36. Roberto Natalini, Andrea Plazzi (Eds.), “Comics&Science, The Women in Math Issue” (inside the comics stories “Sofia Kovalevskaby Alice Milani and “E.G.M.O., Operazione paninoby Claudia Flandoli), Edizioni CNR, April 2018.

    37. Roberto Natalini, Mathematics as a positive mental place - An interview with Gigliola Staffilani, EMS Newsletter, June 2018, pp. 19–21. EN

    38. Printed column on the magazine “Sapere”, “Homo Matematicus”, february 2014 – present. (6 articles per year).

    39. Francesco Artibani, Roberto Natalini (Plot), Francesco Artibani (Script) Valerio Held (Artworks), Topolino e i numeri del futuro (Mickey Mouse and the numbers from the future), Topolino Magazine n. 3279, September 26th, 2018.

    40. Roberto Natalini, Andrea Plazzi (Eds.), “Comics&Science, The Light Issue” (inside the comics story “Educazione subatomica” by Zerocalcare), Edizioni CNR, October 2018.