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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).

Preprints:

  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).

Papers:

  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.