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 γ which may in particular decay in an arbitrary way at infinity. Assuming further that γ is non-increasing and decays sufficiently slowly at infinity, in the sense that γ(s)∼s−k as s→∞ for some k∈(0,N/(N−2)+), it is also shown that global solutions are uniformly bounded with respect to time. The admissible decay of γ at infinity here is higher than in previous works.