11 citations · 14 across the 19 of their papers we have counts for
6 papers · 2 filters
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…