Global bounded classical solutions to a parabolic–elliptic chemotaxis model with local sensing and asymptotically unbounded motility

Abstract Global existence and boundedness of classical solutions are shown for a parabolic–elliptic chemotaxis system with local sensing when the motility function is assumed to be unbounded at infinity. The cornerstone of the proof is the derivation of ‐estimates on the second component of the system and is achieved by various comparison arguments.