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Abstract

In this paper, we will consider blowup solutions to the so called Keller–Segel system and its simplified form. The Keller–Segel system was introduced to describe how cellular slime molds aggregate, owing to the motion of the cells toward a higher concentration of a chemical substance produced by themselves. We will describe a common conjecture in connection with blowup solutions to the Keller–Segel system, and some results for solutions to simplified versions of the Keller–Segel system, giving the evidence that the conjecture is true.