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

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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

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詳細情報 詳細情報について

  • CRID
    1390290699772163840
  • NII論文ID
    120006459662
  • DOI
    10.14943/84115
  • HANDLE
    2115/69775
  • 本文言語コード
    en
  • データソース種別
    • JaLC
    • IRDB
    • CiNii Articles
  • 抄録ライセンスフラグ
    使用可

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