187 citations · 1.1k across the 80 of their papers we have counts for
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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…
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,…
Structured Model Conserving Biomass for the Size-spectrum Evolution in Aquatic Ecosystems
Laura Kanzler, Benoit Perthame, Benoit Sarels
Mathematical modelling of the evolution of the size-spectrum dynamics in aquatic ecosystems was discovered to be a powerful tool to have a deeper insight into impacts of human- and…
Collective motion driven by nutrient consumption
Pierre-Emmanuel Jabin, Benoît Perthame
A classical problem describing the collective motion of cells, is the movement driven by consumption/depletion of a nutrient. Here we analyze one of the simplest such model written…
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…