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

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.