Research leading to some of the publications listed on this page was supported
by the National Science Foundation through grants:
NSF CAREER DMS-1514761 (2016-2021), DMS-1412748 (2014-2017),
DMS-1109682 (2011-2014), DMS-0807636 (2008-2011)
and by the Feodor-Lynen Fellowship (2006-2007).

    F. Golse, M. Gualdani, C. Imbert and A. Vasseur.
      Regularity for the homogeneous Landau-Coulomb equation.
      In preparation

    L. Caffarelli, M. Gualdani and N. Zamponi.
      A nonlocal porous media equation . Submitted

    M.P. Gualdani and N. Guillen.
      On Ap weights and the Landau equations.
    To Appear in Calc. Var. and PDEs (2018)

    M.P. Gualdani and N. Zamponi.
      Global existence of weak even solutions for an isotropic Landau equation with Coulomb potential.
      SIAM J. Math. Anal. 50 (2018), no. 4, 3676 -3714.

    M.P. Gualdani and N. Zamponi.
      A Review on an isotropic Landau model To appear in Springer INdAM Series, Springer (2018)

    M.P. Gualdani and N. Zamponi.
      Spectral gap and exponential convergence to equilibrium for a multi-species Landau system. Bull. Sci. Math. 141 (2017), no. 6, 509 - 538.

    M.P.Gualdani, S. Mischler and C. Mouhot.
      Factorization for non-symmetric operators and exponential H-theorem.
      Memoires de la SMF 153 (2017), 137 pages.

    M.P. Gualdani and N. Guillen.
      Estimates for radial solutions of the homogeneous Landau equation with Coulomb potential. Analysis & PDE, Vol. 9 (2016), No. 8, 1772 - 1809.

    M.d.M Gonzalez, M.P. Gualdani and J.Sola-Morales.
      Instability and bifurcation in a trend depending price formation model. Acta Appl. Math. 144 (2016), 121-136.

    M.P. Gualdani, M.d.M Gonzalez and H. Shahgholian.
      A discrete Bernoulli free boundary problem.
     Proceedings of the St. Petersburg Mathematical Society, Volume XV:
     Advances in Mathematical Analysis of Partial Differential Equations, (2014) 119-140.

    J. A. Carrillo, M.d.M Gonzalez, M.P.Gualdani and M.E. Schonbek.
      Classical Solutions for a nonlinear Fokker-Planck equation arising in Computational Neuroscience.
      Comm. Partial Differential Equations 38 (2013), no. 3, 385 - 409.

    A. Arnold, I.M.Gamba, M.P.Gualdani, S. Mischler, C. Mouhot and C. Sparber.
      The Wigner-Fokker-Planck equation: Stationary states and large time behavior.
      Math. Models Methods Appl. Sci. 22 (2012), no. 11, 1250034 -1250065.

    M.d.M Gonzalez, M.P. Gualdani.
      Some non-standard Sobolev spaces: interpolation and its application to PDE.
      Acta Appl. Math. 121 (2012), 57-67.

    M.d.M Gonzalez, M.P. Gualdani.
      Asymptotics for a free-boundary problem in price formation.
      Nonlinear Analysis 74 (2011), pp. 3269-3294.

    L. Chayes, M.d.M Gonzalez, M.P. Gualdani and I. Kim.
      Global existence and uniqueness of solutions to a model in price formation.
      SIAM J. Math. Anal. Volume 41, Issue 5, pp. 2107-2135 (2009).

    I.M. Gamba, M.P. Gualdani, C. Sparber.
      A note on the time-decay of solutions for the linearized Wigner-Poisson system.
      Kinetic and Related Models, Volume: 2, Number: 1, March 2009.

    I.M. Gamba, M. P. Gualdani and P. Zhang.
      On the blowing up of solutions to a quantum hydrodynamic model on a bounded domain.
      Monats. Math. 157 (2009), no. 1, 37-54.

    I.M. Gamba, M.P. Gualdani and R. Sharp.
      An Adaptable Discontinuous Galerkin Scheme for the Wigner-Fokker-Planck Equation.
      Comm. Math. Sci. (2009) Vol. 7, No.3, 635-664.

    M.d.M Gonzalez, M.P. Gualdani.
      Asymptotics for a symmetric equation in price formation.
      Applied Mathematics and Optimization: Volume 59, Issue 2 (2009), Page 233-246.

    J. A. Carrillo, M. P. Gualdani, and A. Jüngel.
      Convergence of an entropic semi-discretization for nonlinear Fokker-Planck equations in R^d.
      Publ. Mat. 52 (2008), 413-433.

    J. A. Carrillo, M. Di Francesco, M. P. Gualdani.
      Semidiscretization and long-time asymptotics of nonlinear diffusion equations.
      Comm. Math. Sci. Supplemental Issue, No.1, 21-53 (2007).

    M. P. Gualdani, A. Jüngel, G. Toscani.
      A nonlinear fourth-order parabolic equation with non-homogeneous boundary conditions.
      SIAM J. Math. Anal. 37 (2006), No. 6, 1761-1779.

    J. A. Carrillo, M. P. Gualdani, G. Toscani.
      Finite speed of propagation in porous media by mass transportation methods.
      C. R. Acad. Sci. Paris, Ser. I 338 (2004) 815-818.

    M. P. Gualdani, A. Jüngel.
      Analysis of the viscous quantum hydrodynamic equations for semiconductors.
      Europ. J. Appl. Math., (2004) vol. 15, 577-595.

    M. P. Gualdani, A. Jüngel, and G. Toscani.
      Exponential decay in time of solutions of the viscous quantum hydrodynamic equations.
      Appl. Math. Lett. 16 (2003), 1273-1278.

    M. P. Gualdani.
      On a Mathematical model for the crystallization of Polymers.
      Bollettino U.M.I. (8) 6-B (2003), 161-179.


    M.P. Gualdani, X. Ren and I. Sorribes.
      Global well-posedness for a mathematical model in tumor growth.

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