11 citations · 14 across the 19 of their papers we have counts for
6 papers · 1 filter
A Li-Yau and Aronson-Bénilan approach for the Keller-Segel system with critical exponent
Charles Elbar, Alejandro Fernández-Jiménez, Filippo Santambrogio
The Li-Yau and Aronson-Bénilan estimates are fundamental differential inequalities for heat and porous-medium equations, yielding differential Harnack inequalities and sharp smooth…
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…
A cross-diffusion system with independent drifts and fast diffusion
Charles Elbar, Filippo Santambrogio
We study a one-dimensional cross-diffusion system for two interacting populations on the torus, with a fast-diffusion law with exponent and different external potential…
Rate of Convergence for a Nonlocal-to-local Limit in One Dimension
José A. Carrillo, Charles Elbar, Stefano Fronzoni +1
We consider a nonlocal approximation of the quadratic porous medium equation where the pressure is given by a convolution with a mollification kernel. It is known that when the ker…
Weak solutions and sharp interface limit of the anisotropic Cahn-Hilliard equation with disparate mobility and inhomogeneous potential
Charles Elbar, Andrea Poiatti
We study the existence of weak solutions and the corresponding sharp interface limit of an anisotropic Cahn-Hilliard equation with disparate mobility, i.e., the mobility is degener…