Extensibility criterion ruling out gradient blow-up in a quasilinear degenerate chemotaxis system with flux limitation
This paper deals with a quasilinear degenerate chemotaxis system with flux limitation, under no-flux boundary conditions in the balls, and the initial condition for a radially symmetric and positive initial data. \textit{N. Bellomo} and \textit{M. Winkler} [Commun. Partial Differ. Equations 42, No. 3, 436--473 (2017; Zbl 1430.35166)] proved local existence of unique classical solutions and extensibility criterion ruling out gradient blow-up as well as global existence and boundedness of solutions when \(p=q=1\) under some conditions. This paper derives local existence and extensibility criterion ruling out gradient blow-up when \(p,q\ge 1\), and moreover shows global existence and boundedness of solutions when \(p>q+1-\frac{1}{n}\).
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