3 papers
math.AP2020
A hyperbolic-elliptic-parabolic PDE model describing chemotactic E. coli colonies
Danielle Hilhorst, Pierre Roux
We study a modified version of an initial-boundary value problem describing the formation of colony patterns of bacteria \textit{Escherichia Coli}. The original system of three par…
math.AP2020
Mathematical treatment of PDE model describing chemotactic E. coli colonies
Rafał Celiński, Danielle Hilhorst, Grzegorz Karch +2
We consider an initial-boundary value problem describing the formation of colony patterns of bacteria Escherichia coli. This model consists of reaction-diffusion equations coupled…
math.AP2018
Global-in-time classical solutions and qualitative properties for the NNLIF neuron model with synaptic delay
María J. Cáceres, Pierre Roux, Delphine Salort +1
The Nonlinear Noisy Leaky Integrate and Fire (NNLIF) model is widely used to describe the dynamics of neural networks after a diffusive approximation of the mean-field limit of a s…