19 citations · 50 across the 31 of their papers we have counts for
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The fuzzy Landau equation: global well-posedness and Fisher information
Maria Pia Gualdani, Nestor Guillen, Nataša Pavlović +2
We investigate a fuzzy variant of the inhomogeneous Landau equation and establish global-in-time existence and uniqueness of smooth solutions for a range of soft potentials. The sp…
Fractional cross-diffusion in a bounded domain: existence, weak-strong uniqueness, and long-time asymptotics
Nicola De Nitti, Nicola Zamponi
We study a fractional cross-diffusion system that describes the evolution of multi-species populations in the regime of large-distance interactions in a bounded domain. We prove ex…
A quasilinear Keller-Segel model with saturated discontinuous advection
Maria Gualdani, Mikel Ispizua, Nicola Zamponi
We consider the singular limit of a chemotaxis model of bacterial collective motion recently introduced in arXiv:2009.11048 [math.AP]. The equation models aggregation-diffusion phe…
Global weak solutions for a nonlocal multispecies Fokker-Planck-Landau system
Jingwei Hu, Ansgar Jüngel, Nicola Zamponi
The global-in-time existence of weak solutions to a spatially homogeneous multispecies Fokker-Planck-Landau system for plasmas in the three-dimensional whole space is shown. The Fo…
Partial Hölder Regularity for Solutions of a Class of Cross-Diffusion Systems with Entropy Structure
Marcel Braukhoff, Claudia Raithel, Nicola Zamponi
In this article we show a -partial regularity result for solutions of a certain class of cross-diffusion systems with entropy structure. Under slightly more stringent cond…
Three-species drift-diffusion models for memristors
Clément Jourdana, Ansgar Jüngel, Nicola Zamponi
A system of drift-diffusion equations for the electron, hole, and oxygene vacancy densities in a semiconductor, coupled to the Poisson equation for the electric potential, is analy…
Global weak solutions to the compressible Cucker-Smale-Navier-Stokes system in a bounded domain
Li Chen, Yue Li, Nicola Zamponi
A coupled kinetic-fluid model is investigated, which describes the dynamic behavior of an ensemble of Cucker-Smale flocking particles interacting with a viscous fluid in a three-di…
Analysis of a fractional cross-diffusion system for multi-species populations
Ansgar Jüngel, Nicola Zamponi
The global in time existence of weak solutions to a cross-diffusion system with fractional diffusion in the whole space is proved. The equations describe the evolution of multi-spe…
Connection between a degenerate particle flow model and a free boundary problem
Li Chen, Simone Göttlich, Nicola Zamponi
In this paper a strongly degenerate parabolic equation derived from a density dependent particle flow model is studied. Furthermore, a free boundary problem and its connection to t…
Global weak solutions to the Vlasov-Poisson-Fokker-Planck-Navier-Stokes system
Li Chen, Fucai Li, Yue Li +1
We consider the compressible Vlasov-Poisson-Fokker-Planck-Navier-Stokes system in a three dimensional bounded domain with nonhomogeneous Dirichlet boundary conditions. The system d…
Analysis and mean-field derivation of a porous-medium equation with fractional diffusion
Li Chen, Alexandra Holzinger, Ansgar Jüngel +1
A mean-field-type limit from stochastic moderately interacting many-particle systems with singular Riesz potential is performed, leading to nonlocal porous-medium equations in the…
Existence of smooth solutions to the Landau-Fermi-Dirac equation with Coulomb potential
William Golding, Maria Pia Gualdani, Nicola Zamponi
In this paper, we prove global-in-time existence and uniqueness of smooth solutions to the homogeneous Landau-Fermi-Dirac equation with Coulomb potential. The initial conditions ar…
Nonisothermal Richards flow in porous media with cross diffusion
Esther S. Daus, Josipa Pina Milišić, Nicola Zamponi
The existence of large-data weak entropy solutions to a nonisothermal immiscible compressible two-phase unsaturated flow model in porous media is proved. The model is thermodynamic…
Non-Local Porous Media Equations with Fractional Time Derivative
Esther S. Daus, Maria Pia Gualdani, Jingjing Xu +2
In this paper we investigate existence of solutions for the system: \begin{equation*} \left\{ \begin{array}{l} D^α_tu=\textrm{div}(u \nabla p),\\ D^α_tp=-(-Δ)^{s}p+u^{2}, \end{arra…
Analysis of a cross-diffusion model for rival gangs interaction in a city
Alethea B. T. Barbaro, Nancy Rodriguez, Havva Yoldaş +1
We study a two-species cross-diffusion model that is inspired by a system of convection-diffusion equations derived from an agent-based model on a two-dimensional discrete lattice.…
Existence analysis of a degenerate diffusion system for heat-conducting fluids
Gianluca Favre, Ansgar Jüngel, Christian Schmeiser +1
The existence of global weak solutions to a parabolic energy-transport system in a bounded domain with no-flux boundary conditions is proved. The model can be derived in the diffus…
Partial Hölder Regularity for Bounded Solutions of a Class of Cross-Diffusion Systems with Entropy Structure
Marcel Braukhoff, Claudia Raithel, Nicola Zamponi
In this contribution we obtain partial -regularity for bounded solutions of a certain class of cross-diffusion systems, which are strongly coupled, degenerate quasilinear…
Existence analysis of a stationary compressible fluid model for heat-conducting and chemically reacting mixtures
Miroslav Buliček, Ansgar Jüngel, Milan Pokorný +1
The existence of large-data weak solutions to a steady compressible Navier-Stokes-Fourier system for chemically reacting fluid mixtures is proved. General free energies are conside…
Global existence for a two-phase flow model with cross diffusion
Esther S. Daus, Josipa-Pina Milišić, Nicola Zamponi
In this work we study a degenerate pseudo-parabolic system with cross diffusion describing the evolution of the densities of an unsaturated two-phase flow mixture with dynamic capi…
Longtime behavior and weak-strong uniqueness for a nonlocal porous media equation
Esther S. Daus, Maria Gualdani, Nicola Zamponi
In this manuscript we consider a non-local porous medium equation with non-local diffusion effects given by a fractional heat operator \begin{equation*} \partial_t u = \mbox{div}(u…
Analysis of a degenerate and singular volume-filling cross-diffusion system modeling biofilm growth
Esther S. Daus, Josipa-Pina Milišić, Nicola Zamponi
We analyze the mathematical properties of a multi-species biofilm cross-diffusion model together with very general reaction terms and mixed Dirichlet-Neumann boundary conditions on…
Existence of weak solutions to a continuity equation with space time nonlocal Darcy law
Luis Caffarelli, Maria Gualdani, Nicola Zamponi
In this manuscript we consider a porous medium equation with non-local diffusion effects given by a fractional heat operator in two space dimensions. Global i…
A review for an isotropic Landau model
Maria Gualdani, Nicola Zamponi
We consider the equation $u_t = \mbox{Div}(a[u]\nabla u - u\nabla a[u])$, . This model has attracted some attention in the recents years and several results are available…
Global existence of weak even solutions for an isotropic Landau equation with Coulomb potential
Maria Gualdani, Nicola Zamponi
In this manuscript we consider an isotropic modification for the Landau equation with Coulomb potential in three space dimensions. Global in time existence of weak solutions for ev…