Refined Asymptotic Behavior of Blowup Solutions to a Simplified Chemotaxis System

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,...

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Bibliographic Details
Published inCommunications on Pure and Applied Mathematics Vol. 75; no. 8; pp. 1870 - 1886
Main Author Mizoguchi, Noriko
Format Journal Article
LanguageEnglish
Japanese
Published Melbourne Wiley 01.08.2022
John Wiley & Sons Australia, Ltd
John Wiley and Sons, Limited
Subjects
Asymptotic properties
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Summary: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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ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.21954