Boundedness of solutions to a quasilinear parabolic–parabolic chemotaxis model with nonlinear signal production.

Abstract This work is concerned with a quasilinear parabolic–parabolic chemotaxis model with nonlinear signal production: u t = ∇ ⋅ ((1 + u) − α ∇ u) − ∇ ⋅ (u (1 + u) β − 1 ∇ v) + f (u) , v t = Δ v − v + u γ , with nonnegative initial data under homogeneous Neumann boundary conditions in a smooth bounded domain, where α , β ∈ R and γ > 0. The logistic type source term f (u) satisfies that either f (u) ≡ 0 or f (u) = r u − μ u k with r ∈ R , μ > 0 and k > 1. The global-in-time existence and uniform-in-time boundedness of solutions are established under specific parameters conditions, which improves the known results. [ABSTRACT FROM AUTHOR]