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Asymptotic behavior of type I blowup solutions to a parabolic-elliptic system of drift-diffusion type

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Title: Asymptotic behavior of type I blowup solutions to a parabolic-elliptic system of drift-diffusion type
Authors: Yoshikazu, Giga Browse this author
Noriko, Mizoguchi Browse this author
Takasi, Senba Browse this author
Issue Date: 3-Sep-2010
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 968
Start Page: 1
End Page: 30
Abstract: A Cauchy problem for a parabolic-elliptic system of drift-di usion type is considered. The problem is formally of the form Ut = r (rU 􀀀 Ur(􀀀 )􀀀1U): This system describes a mass-conserving aggregation phenomenon including gravitational collapse and bacterial chemotaxis. Our concern is the asymptotic behavior of blowup solutions when the blowup is type I in the sense that its blowup rate is the same as the corresponding ordinary di erential equation yt = y2 (up to a multiple constant). It is shown that all type I blowup is asymptotically (backward) self-similar provided that the solution is radial, nonnegative when the blowup set is a singleton and the space dimension is greater than or equal to three. 2000 Mathematics Subject Classi cation. 35K55, 35K57, 92C17. 1
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69775
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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