A refined asymptotic result of one-dimensional flux limited Keller–Segel models

Abstract

In this paper, we consider a flux-limited Keller–Segel model derived in [16, 18] in a one-dimensional bounded domain and give a refined asymptotic result of the spiky steady state by using the Sturm oscillation theorem in a more meticulous way based on the existence result of spiky steady state in [4], showing a more accurate characterization of the cell aggregation phenomenon.

Keywords

• Flux-limited Keller–Segel model
• spiky steady states
• Sturm oscillation theorem