Roberto Natalini

Elenco delle principali pubblicazioni/List of main publications


Preprints and papers in preparation

  1. Roberto Natalini, Maria Grazia Notarangelo, Emanuela Signori, A mathematical model of intracellular transport including microtubules and RAN cycle in gene anti-tumoral vaccine transfer, in preparation.

  2. A.L. Amadori, R. Natalini, D. Palmigiani, A rare mutation model in heterogeneous environment with simulations for the hawk and dove game, arXiv:1611.10236.

  3. R.. Bianchini, R. Natalini, The paradifferential approach to the local well-posedness of some problems in mixture theory in two space dimensions, submitted (a preliminary version can be found here: https://arxiv.org/abs/1610.03956).

  4. Francois Bouchut, Yann Jobic, Roberto Natalini, René Occelli, Vincent Pavan, Second-order entropy satisfying BGK-FVS schemes for incompressible Navier-Stokes equations, preprint June 2016, submitted (a preprin version can be found here https://hal-upec-upem.archives-ouvertes.fr/hal-01337030)

  5. Roberta Bianchini, Roberto Natalini, Well-posedness of a model of nonhomogeneous compressible-incompressible fluids, preprint June 2016, submitted.

  6. Gabriella Bretti, Roberto Natalini, On modeling Maze solving ability of slime mold via a hyperbolic model of chemotaxis, arXiv:1601.01137, submitted

  7. Ezio Di Costanzo, Roberto Natalini, A hybrid mathematical model of collective motion under alignment and chemotaxis, arXiv:1507.02980.


Journals

  1. 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), arXiv:1512.07033. To appear in Mathematical Medicine And Biology: A Journal of the Ima (2017).

  2. M.P. Bracciale, G. Bretti, A. Broggi, M. Ceseri, A. Marrocchi, R. Natalini, C. Russo, Crystallization Inhibitors: Explaining Experimental Data through Mathematical Models, arXiv:1501.05835. To appear in Applied Mathematical Modelling.(2017).

  3. 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, to appear in Math. Biosci.(2017)

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

  5. 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 2016; doi:10.1093/imammb/dqv024

  6. 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

  7. 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.

  8. 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.

  9. 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. http://dx.doi.org/10.1137/140997099

  10. Anna Lisa Amadori, Antonella Calzolari, Roberto Natalini, Barbara Torti, Rare mutations in evolutionary dynamics, Journal of Differential Equations, 259 (11), 6191-6214. http://dx.doi.org/10.1016/j.jde.2015.07.021.

  11. 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

  12. 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

  13. 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.

  14. 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.

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

  16. 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

  17. 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).

  18. 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.

  19. 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.

  20. 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.

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

  22. 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.

  23. 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.

  24. 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

  25. 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.

  26. 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.

  27. 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

  28. 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.

  29. 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.

  30. 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.

  31. 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.

  32. 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.

  33. 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.

  34. 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.

  35. 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.

  36. 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.

  37. 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.

  38. 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.

  39. 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.

  40. 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.

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

  42. 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.

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

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

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

  46. 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.

  47. 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.

  48. 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.

  49. 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).

  50. 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).

  51. 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.

  52. 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.

  53. 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.

  54. 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.

  55. 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).

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

  57. 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.

  58. 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.

  59. 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.

  60. 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.

  61. 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.

  62. 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.

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

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

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

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

  67. 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.

  68. 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.

  69. 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.

  70. Luo, Tao; Natalini, Roberto; Xin, Zhouping Large time behavior of the solutions to a hydrodynamic model for semiconductors. SIAM J. Appl. Math. 59 (1999), no. 3, 810—830.

  71. 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.

  72. 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.

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

  74. 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.

  75. 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.

  76. 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.

  77. 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.

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

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

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

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

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

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

  84. 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.

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

  86. 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.

  87. 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.

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

  89. 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).

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

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

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

  93. 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.

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

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);

Proceedings e short refereed papers

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

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

  10. 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/j.cam.2006.10.057 Published: DEC 31 2007.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  21. 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.

  22. 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.

  23. 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.

  24. 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.

  25. 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.

  26. 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.

  27. 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.

  28. 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.

  29. 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.