Application of the best constant of the Sobolev inequality to degenerate Keller-Segel models

Yoshie Sugiyama

研究成果: ジャーナルへの寄稿学術誌査読

40 被引用数 (Scopus)

抄録

We consider the degenerate Keller-Segel system (KS)m with 1 < m ≤ 2-2/N of Nagai type below. Our aim is to find the two types of conditions on the initial data which divide the situation of the solution (u, v) into the global existence and the finite time blow-up; one is the assumption on the size of the other one is the assumption on the size of ∂ u0 N(2-m)/2 dx. Moreover, we discuss the critical case of m = 2-2/N (N ≥ 3). We find the upper bound and the lower bound on the size of the L1(= L N(2-m)/2 )-norm of the initial data which assures the global existence and the finite time blowup, respectively. Our results cover the well-known threshold number 8π/αχ in R2 for the semi-linear case, since both bounds correspond to 8π/αχ by substituting m = 1 and N = 2 formally. For our main results, we also give a proof of the mass conservation law in ℝN to (KS)m.

本文言語英語
ページ(範囲)121-144
ページ数24
ジャーナルAdvances in Differential Equations
12
2
出版ステータス出版済み - 12月 1 2007

!!!All Science Journal Classification (ASJC) codes

  • 分析
  • 応用数学

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