2 papers
math.AP2024
Noisy integrate-and-fire equation: continuation after blow-up
Xu'An Dou, Benoît Perthame, Delphine Salort +1
The integrate and fire equation is a classical model for neural assemblies which can exhibit finite time blow-up. A major open problem is to understand how to continue solutions af…
math.AP2023
Incompressible limit of porous media equation with chemotaxis and growth
Qingyou He, Hai-Liang Li, Benoît Perthame
We revisit the problem of proving the incompressible limit for the compressible porous media equation with Newtonian drift and growth. The question is motivated by models of living…