Abstract
This work establishes an indirect chemotaxis model with diffusion-dependent signal concentration { ut = Δ(uγ(v)), vt = Δv – v + w, wt = Δw – w + u for all (x,t) ∈ Ω × (0,∞), in a smooth bounded domain Ω ⊂ ℝ2 under the homogeneous second boundary condition, and the positive function γ fulfills assumptions: γ(s) ∈ C3([0,∞)) and γ′(s) ≤ 0 (∀s > 0). By some prior estimation, the boundedness of solutions can be obtained from this model.
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