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:
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J. Hu, A. Jüngel, N. Zamponi.
Global weak solutions for a nonlocal multispecies Fokker-Planck-Landau system.
arXiv: 2305.17447.
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L. Chen, S. Göttlich, N. Zamponi.
Connection between a degenerate particle flow model and a free boundary problem.
arXiv: 2202.04416.
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E. S. Daus, J.-P. Milišić, N. Zamponi.
Nonisothermal Richards flow in porous media with cross diffusion.
arXiv: 2102.00455.
Papers:
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C. Jourdana, A. Jüngel, N. Zamponi.
Three-species drift-diffusion models for memristors.
To appear in Mathematical Models and Methods in Applied Sciences.
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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.
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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.
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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.
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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.
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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.
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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.
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A. Jüngel, N. Zamponi.
Analysis of a fractional cross-diffusion system for multi-species populations.
Journal of Differential Equations 322 (2022): 237-267.
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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.
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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.
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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.
- 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.
- 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.
- 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.
- 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.
- G. Dhariwal, A. Jüngel, N. Zamponi.
Global martingale solutions for a stochastic population cross-diffusion system.
Stochastic Process. Appl. 129.10 (2019): 3792-3820.
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M. Gualdani, N. Zamponi.
A review for an isotropic Landau model.
PDE models for multi-agent phenomena, Springer INdAM Series 28 (2018): 115-144.
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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.
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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.
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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.
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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.
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A. Jüngel, P. Shpartko, N. Zamponi.
Energy-transport models for spin
transport in ferromagnetic semiconductors.
Commun. Math. Sci. 15.6 (2017): 1527-1563.
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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.
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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.
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A. Jüngel, N. Zamponi.
Qualitative behavior of solutions to
cross-diffusion systems from population dynamics.
Journal of Math. Anal. Appl. 440 (2016): 794-809.
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N. Zamponi, A. Jüngel.
Analysis of a coupled spin drift-diffusion
Maxwell-Landau-Lifshitz system.
Journal of Differential Equations
260 (2016): 6828-6854.
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S. Daus, A. Jüngel, C. Mouhot, N. Zamponi.
Hypocoercivity for a
linearized multi-species Boltzmann system.
SIAM J. Math. Anal. 48 (2016): 538-568.
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N. Zamponi, A. Jüngel.
Global existence analysis for degenerate
energy-transport models for semiconductors.
Journal of Diff. Eq. 2015, vol. 258, 2339 - 2363.
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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.
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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.
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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.
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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).