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

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)


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