The solutions of the quasilinear Keller-Segel system with the volume filling effect do not blow up whenever the Lyapunov functional is bounded from below
Volume 74 / 2006
Banach Center Publications 74 (2006), 127-132
MSC: 92C17, 35K60, 35K57.
DOI: 10.4064/bc74-0-7
Abstract
In \cite{ja:2} we proved two kinds of mechanisms of preventing the blow up in a quasilinear non-uniformly parabolic Keller-Segel systems. One of them was a priori boundedness from below of the Lyapunov functional. In fact, we were able to present a condition under which the Lyapunov functional is bounded from below and a solution exists globally. In the present paper we prove that whenever the Lyapunov functional is bounded from below the solution exists globally.
