Global strong solution to the semi-linear Keller-Segel system of parabolic-parabolic type with small data in scale invariant spaces

Hideo Kozono, Yoshie Sugiyama

研究成果: Contribution to journalArticle査読

26 被引用数 (Scopus)

抄録

We shall show existence of global strong solution to the semi-linear Keller-Segel system in Rn, n ≥ 3, of parabolic-parabolic type with small initial data u0 ∈ Hfrac(n, r) - 2, r (Rn) and v0 ∈ Hfrac(n, r), r (Rn) for max {1, n / 4} < r < n / 2. Our method is based on the perturbation of linealization together with the Lp-Lq estimates of the heat semigroup and the fractional powers of the Laplace operator. As a by-product of our method, we shall prove the decay property of solutions as the time goes to infinity.

本文言語英語
ページ(範囲)1-32
ページ数32
ジャーナルJournal of Differential Equations
247
1
DOI
出版ステータス出版済み - 7 1 2009

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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