Refined Asymptotic Behavior of Blowup Solutions to a Simplified Chemotaxis System

Abstract

Abstract We deal with a parabolic‐elliptic chemotaxis system. It is known that finite‐time blowup occurs for a large class of initial data. However, there have been no results on exact blowup rate or detailed blowup behavior except a special radial solution given just formally in [13] and rigorously in [19, 10, 9]. Our aim is to show that for all radial blowup solutions, their blowup rate, and blowup profile related to mass concentration are the same as those of the special solution. This implies that there is exactly one blowup behavior including blowup rate in radial case . © 2020 Wiley Periodicals LLC.

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