Publications



Research leading to some of the publications listed on this page was supported
by the National Science Foundation through grants:
NSF DMS-2206677 (2022-2025), 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).

    L. Desvillettes, W. Golding, M. Gualdani and A. Loher.
      Production of the Fisher information for the Landau-Coulomb equation with L^1 initial data.
      Preprint.

    M. Gualdani, R. Winter.
      A blow-down mechanism for the Landau-Coulomb equation.
      To appear in Journal Functional Analysis (2025).

    M. Gualdani, M. Ispizua and N. Zamponi.
      A quasilinear Keller-Segel with saturated discontinuous advection.
      Under Review.

    W. Golding, M. Gualdani and A. Loher.
      Global smooth solutions to the Landau-Coulomb equation in L^{3/2}.
      To appear in ARMA.

    M. Bonforte, M. Gualdani and P. Ibarrondo.
      Time-Fractional Porous Medium Type Equations. Sharp Time Decay and Regularization.
      Under Review.

    R. Cabrera, M. Gualdani and N. Guillen.
      Regularization estimates of the Landau-Coulomb diffusion.
      To appear in Nonlinear Analysis (2024)

    W. Golding, M. Gualdani and A. Loher.
      Nonlinear regularization estimates and global well-posedness for the Landau-Coulomb equation near equilibrium.
      To Appear in SIAM Analysis.

    W. Golding, M.P. Gualdani and N. Zamponi.
      Existence of smooth solutions to the Landau-Fermi-Dirac equation with Coulomb potential.
      Commun. Math. Sci. 20 (2022), no. 8, 2315-2365.

    M.P. Gualdani and N. Guillen.
      Hardy's inequality and the isotropic Landau equation.
      J. Funct. Anal. 283 (2022), no. 6, Paper No. 109559.

    J. Bedrossian, M. Gualdani, S. Snelson.
      Non-existence of some approximately self-similar singularities for the Landau, Vlasov-Poisson-Landau, and Boltzmann equations.
      Trans. Amer. Math. Soc. 375 (2022), no. 3, 2187- 2216. https://arxiv.org/pdf/2105.03942.pdf.

    E. Daus, M. Gualdani, J. Xu, N. Zamponi and X. Zhang.
      Nonlocal porous media equations with fractional time derivative.
      Nonlinear Anal. 211 (2021), Paper No. 112486, 35 pp. https://arxiv.org/pdf/2010.16332.pdf.

    F. Golse, M. Gualdani, C. Imbert and A. Vasseur.
      Partial regularity in time for the space homogeneous Landau equation with Coulomb potential.
      Ann. Sci. Ec. Norm. Super. (4) 55 (2022), no. 6, 1575-1611. https://arxiv.org/pdf/1906.02841.pdf.

    J.L. Chern and M. Gualdani.
      Uniqueness of higher integrable solution to the Landau equation with Coulomb interactions.
      Math. Res. Lett. 29 (2022), no. 4, 945-960. https://arxiv.org/pdf/1910.06216.pdf.

    L. Caffarelli, M. Gualdani and N. Zamponi.
      A nonlocal porous media equation.
      Comm. Partial Differential Equations 45 (2020), no. 12, 1799-1819.

    E. Daus, M. Gualdani and N. Zamponi.
      Long time behavior and weak-strong uniqueness for a nonlocal porous media equation.
      J. Differential Equations 268 (2020), no. 4, 1820-1839.

    M.P. Gualdani and N. Guillen.
      On Ap weights and the Landau equations.
    Calc. Var. Partial Differential Equations 58 (2019), no. 1, 58:17

    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.
      PDE models for multi-agent phenomena, 115-144, Springer INdAM Ser., 28, Springer, Cham, 2018.

    M.P. Gualdani and N. Zamponi.
      Spectral gap and exponential convergence to equilibrium for a multi-species Landau system.
      http://arxiv.org/pdf/1602.07135v1.pdf 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.
      http://arxiv.org/pdf/1412.0146.pdf. 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.
      http://arxiv.org/pdf/1306.1116.pdf. 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.




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