Blow‐up in a parabolic–elliptic Keller–Segel system with density‐dependent sublinear sensitivity and logistic source

Abstract

This paper deals with the parabolic–elliptic Keller–Segel system with density‐dependent sublinear sensitivity and logistic source, where is a ball with some R >0 and χ >0, 0< α <1, , μ >0, and κ >1. In the case α =1, Winkler (Z. Angew. Math. Phys.; 2018; 69: 40) discovered the condition for κ such that solutions blow up in finite time. The purpose of the present paper is to find conditions for α and κ such that there exist solutions that blow up in finite time in the case of weak‐chemotactic sensitivity, that is, in the case 0< α <1.

Topics & Concepts