9 papers
Interfaces and non-uniqueness in a cross-diffusion system with independent drifts
Charles Elbar, Guy Parker
We study a one-dimensional cross-diffusion system of two populations. Their densities are diffused with a common pressure that depends on the total density, but are transported by…
Global existence for a system without self-diffusion and different mobilities
Charles Elbar
We study a one-dimensional cross-diffusion system for two interacting populations on the torus, with a linear pressure law and different mobilities. For arbitrary bounded non-negat…
Sobolev estimates for the Keller-Segel system and applications to the JKO scheme
Charles Elbar
We prove Sobolev estimates in the Keller-Segel system with linear diffusion in any dimensionby proving a functional inequality, inspired by the Brezis-G…
A Li-Yau and Aronson-Bénilan approach for the Keller-Segel system with critical exponent
Charles Elbar, Alejandro Fernández-Jiménez, Filippo Santambrogio
We prove Li-Yau and Aronson-Bénilan type estimates for the parabolic-elliptic Keller-Segel system with critical exponent , i.e. lower bounds on the Laplacian of a su…
A deterministic particle approximation for a fourth-order equation
Charles Elbar, Alejandro Fernández-Jiménez
We provide a deterministic particle approximation to a fourth order equation with applications in cell-cell adhesion. In order to do that, first we show that the equation can be as…
On a repulsion model with Coulomb interaction and nonlinear mobility
Antonin Chodron de Courcel, Charles Elbar
We study a scalar conservation law on the torus in which the flux is composed of a Coulomb interaction and a nonlinear mobility: $\mathbf{j} = -u^m\nabla\mathsf{g}\ast…