Blowup solutions to some systems related to biology

Abstract

In this paper, we describe blowup solutions to so called Keller-Segel system and its simplified system. Keller-Segel system was introduced to describe the aggregation of cellular slime molds.

We want to investigate blowup solutions to Keller-Segel system. However, it is difficult for us. Then, we investigate solutions to a simplified system of Keller-Segel system, since we can expect that the structure of solutions to the simplified system is similar to the one to Keller-Segel system.

In this paper, we will describe some results for solutions to the simplified system, our conjecture for solutions to Keller-Segel system and the relation between those results and our conjecture.