6 papers
Segregated solutions of a degenerate cross-diffusion system with drifts
Filippo Santambrogio, Simon Schulz
We prove the global existence of segregated weak solutions of a one-dimensional degenerate cross-diffusion system with independent drifts, which is endowed with a Wasserstein gradi…
Fisher information and continuity estimates for nonlinear but 1-homogeneous diffusive PDEs (via the JKO scheme)
Thibault Caillet, Filippo Santambrogio
In this short paper we prove, using the JKO scheme, that quantities such as the Fisher information stay bounded or decrease across time for a family of 1-homogeneous diffusive PDEs…
Uniform regularity estimates for nonlinear diffusion-advection equations in the hard-congestion limit
Noemi David, Filippo Santambrogio, Markus Schmidtchen
We present regularity results for nonlinear drift-diffusion equations of porous medium type (together with their incompressible limit). We relax the assumptions imposed on the drif…
Improved convergence rates for the Hele-Shaw limit in the presence of confining potentials
Noemi David, Alpár R. Mészáros, Filippo Santambrogio
Nowadays a vast literature is available on the Hele-Shaw or incompressible limit for nonlinear degenerate diffusion equations. This problem has attracted a lot of attention due to…
Doubly nonlinear diffusive PDEs: new existence results via generalized Wasserstein gradient flows
Thibault Caillet, Filippo Santambrogio
We prove an existence result for a large class of PDEs with a nonlinear Wasserstein gradient flow structure. We use the classical theory of Wasserstein gradient flow to derive an E…
Sticky-reflecting diffusion as a Wasserstein gradient flow
Jean-Baptiste Casteras, Léonard Monsaingeon, Filippo Santambrogio
In this paper we identify the Fokker-Planck equation for (reflected) Sticky Brownian Motion as a Wasserstein gradient flow in the space of probability measures. The driving functio…