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:
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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.
Submitted for publication (arXiv: 2010.16332).
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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.
Submitted for publication (arXiv: 2009.04189).
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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).
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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).
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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. Submitted for publication (arXiv: 2001.06082).
Papers:
- 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.
- 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. (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.