### A fast blowup solution to an elliptic-parabolic system related to chemotaxis

Takasi Senba

#### Abstract

We consider radial blowup solutions to an elliptic-parabolic system in $N$-dimensional Euclidean space. The system is introduced to describe several phenomena, for example, motion of bacteria by chemotaxis and equilibrium of self-attracting clusters. In the case where $N \geq 3$, we can find positive and radial backward self-similar solutions which blow up in finite time. In the present paper, in the case where $N \geq 11$, we show the existence of a radial blowup solution whose blowup speed is faster than the one of backward self-similar solutions, by using so-called asymptotic matched expansion techniques.

#### Article information

Source
Adv. Differential Equations, Volume 11, Number 9 (2006), 981-1030.

Dates
First available in Project Euclid: 18 December 2012