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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…
Global martingale solutions for a stochastic population cross-diffusion system
Gaurav Dhariwal, Ansgar Jüngel, Nicola Zamponi
The existence of global nonnegative martingale solutions to a stochastic cross-diffusion system for an arbitrary but finite number of interacting population species is shown. The r…
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…