The Keller-Segel system of parabolic-parabolic type with initial data in weak Ln/2(ℝn) and its application to self-similar solutions

Hideo Kozono*, Yoshie Sugiyama

*この研究の対応する著者

研究成果: Article査読

29 被引用数 (Scopus)

抄録

We shall show the existence of a global strong solution to the semilinear Keller-Segel system in ℝn, n ≥ 3 of parabolic-parabolic type with small initial data u0 ∈ Lwn/2 (ℝn) and v0 ∈ BMO. Our method is based on the perturbation of linearization together with the Lp -L q-estimates of the heat semigroup and the fractional powers of the Laplace operator. As a by-product of our method, we shall construct a self-similar solution and prove the smoothing effect. Furthermore, the stability problem on our strong solutions will be also discussed.

本文言語English
ページ(範囲)1467-1500
ページ数34
ジャーナルIndiana University Mathematics Journal
57
4
DOI
出版ステータスPublished - 2008
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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