MR3157147 Takasi SENBA Takasi SENBA Stability of Stationary Solutions and Existence of Oscillating Solutions to a Chemotaxis System in High Dimensional Spaces Funkcialaj Ekvacioj. Serio Internacia 56 2013 339--378 http://fe.math.kobe-u.ac.jp/FE/FullPapers/56-3/56_339.pdf http://www.ams.org/mathscinet-getitem?mr=MR3157147 We consider classical solutions to a parabolic-elliptic system. The system is a simplified version of a chemotaxis model. It is well known that solutions to the system have many kinds of behaviors. If the initial function is sufficiently small in the sense of a suitable functional space, the solution exists globally in time. If the initial function is sufficiently large in the sense of a suitable functional space, the solution blows up in finite time. In addition, there exist solutions blowing up in infinite time. In this paper, we show a stability of radial stationary solutions, and construct oscillating solutions in high dimensional case. Chemotaxis, Stability of stationary solutions, Oscillating solutions. 35K55, 35B40. 56-339 2013 Stability of Stationary Solutions and Existence of Oscillating Solutions to a Chemotaxis System in High Dimensional Spaces Takasi SENBA Takasi SENBA
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