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Research interests and publications

Research Areas:

I focus my research on entropy methods for systems of nonlinear diffusive Partial Differential Equations (PDEs), with particular attention to cross-diffusion and nonlocal diffusion structures. More in general, I am interested in the derivation, analysis and numerics of PDEs describing physical/chemical/biological systems like e.g. population dynamics, chemically reacting fluid mixtures, multiphase flow in porous media, biofilms, charge and spin transport in semiconductors.

Ph.D. Thesis:

N. Zamponi. Quantum fluid models for electron transport in graphene. Ph. D. Thesis in Mathematics at Florence University, Florence, Italy (2013).


  1. E. S. Daus, M. P. Gualdani, J. Xu, N. Zamponi, X. Zhang. Non-Local Porous Media Equations with Fractional Time Derivative. Submitted for publication (arXiv: 2010.16332).
  2. A. B. T. Barbaro, N. Rodriguez, H. Yoldaş, N. Zamponi. Analysis of a cross-diffusion model for rival gangs interaction in a city. Submitted for publication (arXiv: 2009.04189).
  3. G. Favre, A. Jüngel, C. Schmeiser, N. Zamponi. Existence analysis of a degenerate diffusion system for heat-conducting fluids. Submitted for publication (arXiv: 2008.05213).
  4. M. Braukhoff, C. Raithel, N. Zamponi. Partial Hölder Regularity for Bounded Solutions of a Class of Cross-Diffusion Systems with Entropy Structure. Submitted for publication (arXiv: 2007.03561).
  5. M. Bulíček, A. Jüngel, M. Pokorný, N. Zamponi. Existence analysis of a stationary compressible fluid model for heat-conducting and chemically reacting mixtures. Submitted for publication (arXiv: 2001.06082).


  1. L. Caffarelli, M. Gualdani, N. Zamponi. Existence of weak solutions to a continuity equation with space time nonlocal Darcy law. Commun. Partial. Differ. Equ. (2020), 1-21.
  2. E. S. Daus, M. Gualdani, N. Zamponi. Longtime behavior and weak-strong uniqueness for a nonlocal porous media equation. J. Diff. Eq. 268.4 (2020), 1820-1839.
  3. E. S. Daus, J.-P. Milišić, N. Zamponi. Analysis of a degenerate and singular volume-filling cross-diffusion system modeling biofilm growth. SIAM J. Math. Anal. 51.4 (2020), 3569-3605.
  4. E. S. Daus, J.-P. Milišić, N. Zamponi. Global existence for a two-phase flow model with cross diffusion. DCDS-B 25.3 (2020), 957-979.
  5. G. Dhariwal, A. Jüngel, N. Zamponi. Global martingale solutions for a stochastic population cross-diffusion system. Stochastic Process. Appl. 129.10 (2019), 3792-3820.
  6. M. Gualdani, N. Zamponi. A review for an isotropic Landau model. PDE models for multi-agent phenomena, Springer INdAM Series 28 (2018), 115-144.
  7. M. Gualdani, N. Zamponi. Global existence of weak even solutions for an isotropic Landau equation with Coulomb potential. SIAM J. Math. Anal. 50.4 (2018), 3676-3714.
  8. A. Jüngel, J. Mikyška, N. Zamponi. Existence analysis of a single-phase flow mixture model with van der Waals pressure. SIAM J. Math. Anal. 50.1 (2018), 1367-1395.
  9. M. Gualdani, N. Zamponi. Spectral gap and exponential convergence to equilibrium for a multi-species Landau system. Bull. Sci. Math. 141.6 (2017), 509-538.
  10. M. Bulíček, M. Pokorný, N. Zamponi. Existence analysis for incompressible fluid model of electrically charged chemically reacting and heat conducting mixtures. SIAM J. Math. Anal. 49.5 (2017), 3776-3830.
  11. A. Jüngel, P. Shpartko, N. Zamponi. Energy-transport models for spin transport in ferromagnetic semiconductors. Commun. Math. Sci. (2017), 1527-1563.
  12. A. Jüngel, N. Zamponi. A cross-diffusion system derived from a Fokker-Planck equation with partial averaging. Z. Appl. Math. Phys. 68.1 (2017), 28.
  13. N. Zamponi, A. Jüngel. Analysis of degenerate cross-diffusion population models with volume filling. Ann. Inst. H. Poincaré (C) Anal. Non Lin. 34 (2017), 1-29. Erratum.
  14. A. Jüngel, N. Zamponi. Qualitative behavior of solutions to cross-diffusion systems from population dynamics. Journal of Math. Anal. Appl. 440 (2016), 794-809.
  15. N. Zamponi, A. Jüngel. Analysis of a coupled spin drift-diffusion Maxwell-Landau-Lifshitz system. Journal of Differential Equations 260 (2016), 6828-6854.
  16. S. Daus, A. Jüngel, C. Mouhot, N. Zamponi. Hypocoercivity for a linearized multi-species Boltzmann system. SIAM J. Math. Anal. 48 (2016), 538-568.
  17. N. Zamponi, A. Jüngel. Global existence analysis for degenerate energy-transport models for semiconductors. Journal of Diff. Eq. 2015, vol. 258, 2339 - 2363.
  18. N. Zamponi. Analysis of a drift-diffusion model with velocity saturation for spin-polarized transport in semiconductors. Journal of Math. Anal. Appl. 2014, vol. 420, issue 2, 1167 - 1181.
  19. N. Zamponi, A. Jüngel. Two spinorial drift-diffusion models for quantum electron transport in graphene. Communication in Mathematical Sciences 2013, vol. 11, no. 3, 807 - 830.
  20. N. Zamponi. Some fluid-dynamic models for quantum electron transport in graphene via entropy minimization. Kinetic and Related Models 2012, vol. 5, no. 1, 203 - 221.
  21. N. Zamponi, L. Barletti. Quantum electronic transport in graphene: a kinetic and fluid-dynamic approach. Math. Methods Appl. Sci. 2011, 34 807 - 818.