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Asymptotic behavior of type I blowup solutions to a parabolic-elliptic system of drift-diffusion type
| 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 |
| Publisher: | Department of Mathematics, Hokkaido University |
| 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
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Submitter: 数学紀要登録作業用
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