# A generalization of the Keller-Segel system to higher dimensions from a structural viewpoint

## Main Article Content

## Abstract

We consider initial boundary problems of a two-chemical substances chemotaxis system. In the four-dimensional setting, it was shown that solutions exist globally in time and remain bounded if the total mass is less than (8\pi)^2, whereas the solution emanating from some initial data of large magnitude may blows up.This result can be regarded as a generalization of the well-known 8\pi problem in the Keller--Segel system to higher dimensions. We will compare mathematical structures of the Keller--Segel system and our system and discuss the difference.

## Article Details

How to Cite

Fujie, K., & Senba, T.
(2017).
A generalization of the Keller-Segel system to higher dimensions from a structural viewpoint.

*Proceedings Of Equadiff 2017 Conference,*, 275-282. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/equadiff/article/view/803/574
Section

Articles