Phase transitions and bump solutions of the Keller-Segel model with volume exclusion
Analysis of PDEs
2019-04-29 v1
Abstract
We show that the Keller-Segel model in one dimension with Neumann boundary conditions and quadratic cellular diffusion has an intricate phase transition diagram depending on the chemosensitivity strength. Explicit computations allow us to find a myriad of symmetric and asymmetric stationary states whose stability properties are mostly studied via free energy decreasing numerical schemes. The metastability behavior and staircased free energy decay are also illustrated via these numerical simulations.
Keywords
Cite
@article{arxiv.1904.11937,
title = {Phase transitions and bump solutions of the Keller-Segel model with volume exclusion},
author = {Jose A. Carrillo and Xinfu Chen and Qi Wang and Zhian Wang and Lu Zhang},
journal= {arXiv preprint arXiv:1904.11937},
year = {2019}
}