Boundedness and stability for an indirect signal absorption chemotaxis system with signal-dependent motility

The paper is concerned with a chemotaxis system with indirect signal absorption and signal-dependent motilityunder the homogeneous Neumann boundary condition, where Ω ⊂ R n (n ≥ 1), parameters δ, τ > 0. γ(v) is a motility function.It is shown that in n-dimensional smooth bounded domains with n ≤ 2 or n ≥ 3 and suitable initial data, some appropriate assumptions on γ(v) ensure global existence and stability of a bounded classical solution.