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

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 L infinity$L<^>\infty$-estimates on the second component of the system and is achieved by various comparison arguments.

Automated summary

This article demonstrates the global existence and boundedness of classical solutions for a parabolic-elliptic chemotaxis system with local sensing, assuming that the motility function is unbounded at infinity. The cornerstone of the proof lies in deriving L∞-estimates for the second component of the system by employing various comparison arguments.