Global existence of a quasilinear chemotaxis model with signal-dependent motility and indirect signal production mechanism

Abstract

In this paper, we study the following quasilinear chemotaxis model with signal-dependent motility: nt = Δ(γ(c)nm); ct = dcΔc − c + v; vt = dvΔv − v + n, x ∈ Ω, t > 0, ∂(nmγ(c))∂ν=∂c∂ν=∂v∂ν=0, x ∈ ∂Ω, t > 0, n(x, 0) = n0(x), c(x, 0) = c0(x), v(x, 0) = v0(x), x ∈ Ω, t > 0, where γ(c) = c−r. We show that the above system admits at least one global weak solution.