単純化されたKeller-Segel系の爆発解について(<特集>移流項をもつ反応拡散系)

抄録

The purpose of this article is to describe some properties of solutions to the Keller-Segel model and a simplified Keller-Segel model. The Keller-Segel model was introduced to describe chemotactic aggregation of cellular slime molds, and the simplified Keller-Segel model was also introduced to describe the same phenomenon. Moreover, the simplified Keller-Segel model describes the gravitational interaction of particles. The solutions to those models represent the density of cells or particles. Then, the solutions are functions of spatial and time variables. Those systems have blowup solutions. We say that a solution blows up at finite time, if maximum value of the solution in the spatial domain tends to infinity as time variable tends to the finite time. We think that the blowup corresponds to aggregation of the cells or the particles. In this article, we describe some results about blowup solutions and the relation between those results and the biological phenomenon.