Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis. (English) Zbl 0901.35104

Nagai, Toshitaka; Senba, Takasi; Yoshida, Kiyoshi

Funkc. Ekvacioj, Ser. Int. 40, No. 3, 411-433 (1997).

The Keller-Segel system (KS), a mathematical model describing aggregation of cellular slime models, is studied. In particular, the time global existence and \(L^\infty\) estimate of the solution of (KS) in a bounded domain \(\Omega \subset \mathbb{R}^2\) with smooth boundary \(\partial \Omega\) is examined by using the Trudinger-Moser inequality extended to the Sobolev space \(W^{1,p} (\Omega)\).

Reviewer: S.Totaro (Firenze)

MSC:

35Q80	Applications of PDE in areas other than physics (MSC2000)
46N20	Applications of functional analysis to differential and integral equations

Keywords:

Keller-Segel system; aggregation of cellular slime models; global existence; Trudinger-Moser inequality