11 citations · 14 across the 19 of their papers we have counts for
20 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…
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…
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…
Nonlocal-to-local convergence of the Cahn-Hilliard equation with degenerate mobility and the Flory-Huggins potential
Charles Elbar, Jakub Skrzeczkowski
The Cahn-Hilliard equation is a fundamental model for phase separation phenomena. Its rigorous derivation from the nonlocal aggregation equation, motivated by the desire to link in…
On the limit problem arising in the kinetic derivation of the Cahn-Hilliard equation
Charles Elbar, Benoît Perthame, Jakub Skrzeczkowski
The non-local degenerate Cahn-Hilliard equation is derived from the Vlasov equation with long-range attraction. We study the local limit as the delocalization parameter converges t…
On the inviscid limit connecting Brinkman's and Darcy's models of tissue growth with nonlinear pressure
Charles Elbar, Jakub Skrzeczkowski
Several recent papers have addressed modelling of the tissue growth by the multi-phase models where the velocity is related to the pressure by one of the physical laws (Stoke's, Br…
Nonlocal Cahn-Hilliard equation with degenerate mobility: Incompressible limit and convergence to stationary states
Charles Elbar, Benoît Perthame, Andrea Poiatti +1
The link between compressible models of tissue growth and the Hele-Shaw free boundary problem of fluid mechanics has recently attracted a lot of attention. In most of these models,…
Analysis and numerical simulation of a generalized compressible Cahn-Hilliard-Navier-Stokes model with friction effects
Charles Elbar, Alexandre Poulain
We propose a new generalized compressible diphasic Navier-Stokes Cahn-Hilliard model that we name G-NSCH. This new G-NSCH model takes into account important properties of diphasic…
From nonlocal Euler-Korteweg to local Cahn-Hilliard via the high-friction limit
Charles Elbar, Piotr Gwiazda, Jakub Skrzeczkowski +1
Several recent papers considered the high-friction limit for systems arising in fluid mechanics. Following this approach, we rigorously derive the nonlocal Cahn-Hilliard equation a…
Degenerate Cahn-Hilliard systems: From nonlocal to local
José A. Carrillo, Charles Elbar, Jakub Skrzeczkowski
We provide a rigorous mathematical framework to establish the limit of a nonlocal model of cell-cell adhesion system to a local model. When the parameter of the nonlocality goes to…
Degenerate Cahn-Hilliard equation: From nonlocal to local
Charles Elbar, Jakub Skrzeczkowski
There has been recently an important interest in deriving rigorously the Cahn-Hilliard equation from the nonlocal equation, also called aggregation equation. So far, only non-degen…
From Vlasov equation to degenerate nonlocal Cahn-Hilliard equation
Charles Elbar, Marco Mason, Benoît Perthame +1
We provide a rigorous mathematical framework to establish the hydrodynamic limit of the Vlasov model introduced by Noguchi and Takata in order to describe phase transition of fluid…
Pressure jump and radial stationary solutions of the degenerate Cahn-Hilliard equation
Charles Elbar, Benoît Perthame, Jakub Skrzeczkowski
The Cahn-Hilliard equation with degenerate mobility is used in several areas including the modeling of living tissues. We are interested in quantifying the pressure jump at the int…
Degenerate Cahn-Hilliard and incompressible limit of a Keller-Segel model
Charles Elbar, Benoît Perthame, Alexandre Poulain
The Keller-Segel model is a well-known system representing chemotaxis in living organisms. We study the convergence of a generalized nonlinear variant of the Keller-Segel to the de…