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Research interests and publications


Research Areas:

My research is in the field of nonlinear Partial Differential Equations (PDEs), with particular focus on entropy methods for systems of evolutionary PDEs with degenerate, cross-, and nonlocal diffusion. I am also interested in the derivation and analysis of mathematical models for chemically reacting fluid mixtures.

Preprints:

  1. J. Hu, A. Jüngel, N. Zamponi. Global weak solutions for a nonlocal multispecies Fokker-Planck-Landau system. arXiv: 2305.17447.

  2. L. Chen, S. Göttlich, N. Zamponi. Connection between a degenerate particle flow model and a free boundary problem. arXiv: 2202.04416.

  3. E. S. Daus, J.-P. Milišić, N. Zamponi. Nonisothermal Richards flow in porous media with cross diffusion. arXiv: 2102.00455.

Papers:

  1. C. Jourdana, A. Jüngel, N. Zamponi. Three-species drift-diffusion models for memristors. To appear in Mathematical Models and Methods in Applied Sciences.

  2. L. Chen, Y. Li, N. Zamponi. Global weak solutions to the compressible Cucker-Smale-Navier-Stokes system in a bounded domain. Nonlinear Analysis 232 (2023): 113257.

  3. L. Chen, A. Holzinger, A. Jüngel, N. Zamponi. Analysis and mean-field derivation of a porous-medium equation with fractional diffusion. Commun. Partial. Differ. Equ. 47.11 (2022): 2217-2269.

  4. L. Chen, F. Li, Y. Li, N. Zamponi. Global weak solutions to the Vlasov-Poisson-Fokker-Planck-Navier-Stokes system. Math. Methods Appl. Sci. 46.2 (2023): 2729-2745.

  5. M. Braukhoff, C. Raithel, N. Zamponi. Partial Hölder Regularity for Solutions of a Class of Cross-Diffusion Systems with Entropy Structure. Journal de Mathématiques Pures et Appliquées 166 (2022): 30-69.

  6. M. Bulíček, A. Jüngel, M. Pokorný, N. Zamponi. Existence analysis of a stationary compressible fluid model for heat-conducting and chemically reacting mixtures. Journal of Mathematical Physics 63 (2022): 051501.

  7. W. Golding, M. Gualdani, N. Zamponi. Existence of smooth solutions to the Landau-Fermi-Dirac equation with Coulomb potential. Commun. Math. Sci. 20.8 (2022): 2315-2365.

  8. A. Jüngel, N. Zamponi. Analysis of a fractional cross-diffusion system for multi-species populations. Journal of Differential Equations 322 (2022): 237-267.

  9. E. S. Daus, M. P. Gualdani, J. Xu, N. Zamponi, X. Zhang. Non-Local Porous Media Equations with Fractional Time Derivative. Nonlinear Analysis 211 (2021): 112486.

  10. A. B. T. Barbaro, N. Rodriguez, H. Yoldaş, N. Zamponi. Analysis of a cross-diffusion model for rival gangs interaction in a city. Commun. Math. Sci. 19.8 (2021): 2139-2175.

  11. G. Favre, A. Jüngel, C. Schmeiser, N. Zamponi. Existence analysis of a degenerate diffusion system for heat-conducting fluids. Nonlinear Differential Equations and Applications NoDEA 28.4 (2021): 1-28.

  12. L. Caffarelli, M. Gualdani, N. Zamponi. Existence of weak solutions to a continuity equation with space time nonlocal Darcy law. Commun. Partial. Differ. Equ. 45.12 (2020): 1799-1819.

  13. 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.

  14. 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.

  15. 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.

  16. G. Dhariwal, A. Jüngel, N. Zamponi. Global martingale solutions for a stochastic population cross-diffusion system. Stochastic Process. Appl. 129.10 (2019): 3792-3820.

  17. M. Gualdani, N. Zamponi. A review for an isotropic Landau model. PDE models for multi-agent phenomena, Springer INdAM Series 28 (2018): 115-144.

  18. 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.

  19. 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.

  20. 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.

  21. 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.

  22. A. Jüngel, P. Shpartko, N. Zamponi. Energy-transport models for spin transport in ferromagnetic semiconductors. Commun. Math. Sci. 15.6 (2017): 1527-1563.

  23. 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.

  24. 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.

  25. A. Jüngel, N. Zamponi. Qualitative behavior of solutions to cross-diffusion systems from population dynamics. Journal of Math. Anal. Appl. 440 (2016): 794-809.

  26. N. Zamponi, A. Jüngel. Analysis of a coupled spin drift-diffusion Maxwell-Landau-Lifshitz system. Journal of Differential Equations 260 (2016): 6828-6854.

  27. S. Daus, A. Jüngel, C. Mouhot, N. Zamponi. Hypocoercivity for a linearized multi-species Boltzmann system. SIAM J. Math. Anal. 48 (2016): 538-568.

  28. N. Zamponi, A. Jüngel. Global existence analysis for degenerate energy-transport models for semiconductors. Journal of Diff. Eq. 2015, vol. 258, 2339 - 2363.

  29. 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.

  30. 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.

  31. 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.

  32. N. Zamponi, L. Barletti. Quantum electronic transport in graphene: a kinetic and fluid-dynamic approach. Math. Methods Appl. Sci. 2011, 34 807 - 818.

Ph.D. Thesis:

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