Global existence and uniform boundedness in a chemotaxis model with signal-dependent motility

Abstract

Global existence is established for classical solutions to a chemotaxis model with signal-dependent motility for a general class of motility functions $\gamma$ which may in particular decay in an arbitrary way at infinity. Assuming further that $\gamma$ is non-increasing and decays sufficiently slowly at infinity, in the sense that $\gamma (s)\sim s^{-k}$ as $s\to \infty$ for some $k\in (0,N/(N-2{)}_{+})$, it is also shown that global solutions are uniformly bounded with respect to time. The admissible decay of $\gamma$ at infinity here is higher than in previous works.

arXiv commentarXiv admin note: text overlap with arXiv:2106.02368

References in corpus (4)

• Stripe formation in bacterial systems with density-suppressed motility
• Critical mass on the Keller-Segel system with signal-dependent motility
• Comparison Methods for a Keller--Segel-type Model of Pattern Formations with Density-suppressed Motilities
• Boundedness and Exponential Stabilization in a Parabolic-Elliptic Keller--Segel Model with Signal-dependent Motilities for Local Sensing Chemotaxis

Cited by in corpus (2)

• Global boundedness of solutions to a parabolic-parabolic chemotaxis system with local sensing in higher dimensions
• Asymptotic behavior of a quasilinear Keller--Segel system with signal-suppressed motility