Finite speed of propagation in 1-D degenerate Keller-Segel system

Yoshie Sugiyama

研究成果: ジャーナルへの寄稿学術誌査読

3 被引用数 (Scopus)

抄録

We consider the following Keller-Segel system of degenerate type: (KS): ∂u/∂t = ∂/∂x (∂u m/∂x-u q-1∂v/∂x), x ∈ R{double-struck}, t > 0,0 = ∂ 2v/∂x 2-γν + u,x ∈ R{double-struck}, t > 0, u(x,0)=u 0 (x), x ∈ R{double-struck}, where m > 1, γ > 0, q ≥ 2m. We shall first construct a weak solution u(x, t) of (KS) such that u m - 1 is Lipschitz continuous and such that u m-1+δ for δ > 0 is of class C 1 with respect to the space variable x. As a by-product, we prove the property of finite speed of propagation of a weak solution u(x, t) of (KS), i.e., that a weak solution u(x, t) of (KS) has a compact support in x for all t > 0 if the initial data u 0(x) has a compact support in R{double-struck}. We also give both upper and lower bounds of the interface of the weak solution u of (KS).

本文言語英語
ページ(範囲)744-757
ページ数14
ジャーナルMathematische Nachrichten
285
5-6
DOI
出版ステータス出版済み - 4月 2012
外部発表はい

!!!All Science Journal Classification (ASJC) codes

  • 数学 (全般)

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