PAPERS AUTHORED by Roberto Natalini

    Preprints

  1. 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, IAC Report 160 (7/2008) ; available as pdf-file.

  2. F. Clarelli, R. Natalini, A pressure model of immune response to mycobacterium tuberculosis infection in several space dimensions, IAC Report 145 ; available as pdf-file.

  3. C. Mascia, R. Natalini, On Relaxation Hyperbolic Systems violating the Shizuta-Kawashima condition, IAC Report 126 (5/2007), submitted to ARMA; available as pdf-file.

  4. F. Clarelli, R. Gianni, R. Natalini, A mathematical model for the evolution of nitric oxide concentration in human breathing, IAC Report 102; available as pdf-file.

Papers in Press

  1. 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.

  2. R. Natalini, C. Nitsch, F. Freddi, Mathematical models for damage monitoring and restoration of cultural heritage, to appear in "Proceedings of the IV JSIAM-SIMAI meeting 2005", GAKUTO International Series, Mathematical Sciences and Applications 2008; available as pdf-file.

Selected Published Papers

  1. F. Clarelli, A. Fasano, R. Natalini, Mathematics and monuments conservation: Free boundary models of marble sulphation, SIAM J. Appl. Math. Volume 69, Issue 1, pp. 149-168 (2008),dx.doi.org/10.1137/070695125 ; available as pdf-file.

  2. G. Carbou, B. Hanouzet, R.Natalini, Semilinear behavior for totally linearly degenerate hyperbolic systems with relaxation, Journal of Differential Equations (2008), doi:10.1016/j.jde.2008.05.015 Available online 17 June 2008; available as pdf-file.

  3. D. Aregba-Driollet, M. Briani, R. Natalini Asymptotic high-order schemes for 2x2 dissipative hyperbolic systems, SIAM J. Numer. Anal. 46 (2008), no. 2, 869--894; available as pdf-file.

  4. C.Giavarini, M.L.Santarelli, R.Natalini, F.Freddi, A nonlinear model of sulphation of porous stones: numerical simulations and preliminary laboratory assessments; J. Cultural Heritage 9 (2008), 14-22. Link to the journal page

  5. D. Aregba-Driollet, G. Bretti, R. Natalini, Numerical schemes for the Barenblatt model of non-equilibrium two phase flow in porous media, Quart. Appl. Math. 66 (2008), 201-231; available as pdf-file.

  6. M.F. Carfora, R. Natalini, A discrete kinetic approximation for the incompressible Navier Stokes equations, ESAIM - Mathematical Modelling and Numerical Analysis 42, (2008), 93-112: available as pdf-file.

  7. S. Bianchini, B. Hanouzet, R. Natalini, Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy; Communications Pure Appl. Math. 60 (2007), 1559-1622; available as pdf-file.

  8. 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

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

  10. 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; available as pdf-file.

  11. F.R. Guarguaglini, R. Natalini Nonlinear transmission problems for quasilinear parabolic systems, Networks and Heterogeneous Media 2, n.2 (2007), 359- 381; available as pdf-file.

  12. F. R. Guarguaglini, R. Natalini, Global existence and uniqueness of solutions for multidimensional weakly parabolic systems arising in chemistry and biology, Communications on Pure and Applied Analysis (CPAA) Volume 6, Number: 1 (2007), 287-309; available as pdf-file.

  13. M. Garavello, R. Natalini, B. Piccoli and A. Terracina, Conservation laws with discontinuous, Networks and Heterogeneous Media 2, n.1 (2007), 159 - 179; available as pdf-file.

  14. G. Ali, 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; online from Friday, November 03, 2006; Link to the journal

  15. G. Ali, 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, online from Friday, November 03, 2006; Link to the journal

  16. A. Fasano, R. Natalini, Lost beauties of the Acropolis, what mathematics can say, SIAM News 39 n.6, July/August 2006; available as pdf-file.

  17. 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; available as pdf-file.

  18. 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); available as pdf-file.

  19. 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); available as pdf-file.

  20. 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; available as pdf-file.

  21. F. R. Guarguaglini and R. Natalini, Global existence of solutions to a nonlinear model of sulphation phenomena in calcium carbonate stones, Nonlinear Anal. Real World Appl. 6 (2005), no. 3, 477--494; available as pdf-file.

  22. E. Borrelli, C. Giavarini, M. Incitti, M. L. Santarelli, R. Natalini, A material model for the evolution of gypsum crusts: numerical and experimental results, in ``10th International Congress on Deterioration and Conservation of Stone'', Vol. II, Ed. Daniel Kwiatkowski, Runo L~fvendahl, 27 June- 2 July 2004, Stockholm, Sweden.

  23. 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; available as pdf-file.

  24. 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; available as  pdf-file.

  25. 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); available as  ps-file

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

  27. 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; available as  ps-file

  28.  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; available as  ps-file

  29. 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; available as ps-file

  30. 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. 

  31. 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.

  32. 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.

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

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

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

  36. Gilding, Brian H.; Natalini, Roberto; Tesei, Alberto, How parabolic free boundaries approximate hyperbolic fronts. Trans. Amer. Math. Soc. 352 (2000), no. 4, 1797--1824.  electronically posted on November 18, 1999.

  37. 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.

  38. 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.

  39. 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.

  40. 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. 78Axx (35Qxx 76X05 82Dxx)

  41. 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 35Q99 (35B40 76X05 82D37)

  42. 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. 35L65 (76L05)

  43. 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. 35Q72 (35L60 73F15)

  44. Natalini, Roberto A discrete kinetic approximation of entropy solutions to multidimensional scalar conservation laws. J. Differential Equations 148 (1998), no. 2, 292--317. 35L65 (76P05)

  45. 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. 76L05 (35L60 80A25)

  46. 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. 35L70 (35B60 35D05)

  47. 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. 35L60 (35B35)

  48. 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. 35L60 (35B35)

  49. Natalini, Roberto; Hanouzet, Bernard Weakly coupled systems of quasilinear hyperbolic equations. Differential Integral Equations 9 (1996), no. 6, 1279--1292. 35L60

  50. Aregba-Driollet, Denise; Natalini, Roberto Convergence of relaxation schemes for conservation laws. Appl. Anal. 61 (1996), no. 1-2, 163--193. 65M12 (35L65)

  51. Natalini, Roberto Convergence to equilibrium for the relaxation approximations of conservation laws. Comm. Pure Appl. Math. 49 (1996), no. 8, 795--823. 35L65

  52. Natalini, Roberto; Rubino, Bruno A discrete approximation for hyperbolic systems with quadratic interaction term. Comm. Appl. Nonlinear Anal. 3 (1996), no. 2, 1--21. 35L45 (35A35 65M12 76P05)

  53. Natalini, R. The bipolar hydrodynamic model for semiconductors and the drift-diffusion equations. J. Math. Anal. Appl. 198 (1996), no. 1, 262--281. 35Q99 (82D99)

  54. Kersner, R.; Natalini, R.; Tesei, A. Shocks and free boundaries: the local behaviour. Asymptotic Anal. 10 (1995), no. 1, 77--93. 35R35 (35K55 35L67 76L05 76Rxx)

  55. 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. 65M06 (35Q35 76R50)

  56. Corrias, L.; Falcone, M.; Natalini, R. Numerical schemes for conservation laws via Hamilton-Jacobi equations. Math. Comp. 64 (1995), no. 210, 555--580, S13--S18. 49L25 (35L65 49M25 65K10)

  57. 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. 35Q60 (35D05 35L45 76X05 82D99)

  58. 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. 35K55 (35B40)

  59. Marcati, Pierangelo; Natalini, Roberto Convergence of the pseudo-viscosity approximation for conservation laws. Nonlinear Anal. 23 (1994), no. 5, 621--628. 35L65 (35B25 35L67)

  60. 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. 35L65 (35B05 35B40)

  61. Natalini, Roberto; Tesei, Alberto Blow-up of solutions of first order quasilinear hyperbolic equations. Appl. Anal. 51 (1993), no. 1-4, 81--114. 35L65 (35B05)

  62. Natalini, R. Unbounded solutions for conservation laws with source. Nonlinear Anal. 21 (1993), no. 5, 349--362. 35L65 (35L60)

  63. Natalini, R.; Tesei, A. On a class of perturbed conservation laws. Adv. in Appl. Math. 13 (1992), no. 4, 429--453. 35L65 (35B20)

  64. 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. 35L30

  65. Natalini, Roberto Multiplication de distributions avec conditions de compatibilit�. (French) [Multiplication of distributions with compatibility conditions] Ann. Fac. Sci. Toulouse Math. (5) 10 (1989), no. 1, 75--91. 46F10

    Lecture Notes

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); available as pdf:

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) ; available as ps.gz: