Boundedness for the chemotaxis system in a flux limitation with indirect signal production

A fully parabolic chemotaxis system with indirect signal production u t = Delta u - del <middle dot> ( uf (|del v | (2 ))del v ), x E 12, t > 0, v t = Delta v - v + w, x E 12, t > 0, w t = Delta w - w + u, x E 12, t > 0 is considered in a smooth bounded domain Omega C R (n) ( n > 1) under homogeneous Neumann boundary conditions, where the flux limitation f E C 2 ([0, OO)) is given suitably regular satisfying f ( xi ) < K f (1 + xi ) -alpha for all xi > 0 with some K f > 0 and alpha E R. The range of alpha depending on the dimension n ensures the existence of a global bounded classical solution for the associated initialboundary value problem, in which sense any collapse is excluded. (c) 2024 Elsevier Inc. All rights reserved.