5 papers
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…
Nonisothermal Richards flow in porous media with cross diffusion
Esther S. Daus, Josipa Pina MiliÅ¡iÄ, 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…
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…
The fuzzy Landau equation: global well-posedness and Fisher information
Maria Pia Gualdani, Nestor Guillen, NataÅ¡a PavloviÄ +2
We study a fuzzy variant of the inhomogeneous Landau equation and establish global-in-time existence and uniqueness of smooth solutions for moderately soft potentials. The spatial…
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…