Boundedness of solutions in a chemotaxis system with nonlinear sensitivity and logistic source

This paper deals with a parabolic–elliptic chemotaxis system with nonlinear sensitivity and logistic source{ut=Δu−χ∇⋅(ψ(u)∇v)+f(u),(x,t)∈Ω×(0,∞),0=Δv−v+g(u),(x,t)∈Ω×(0,∞), under homogeneous Neumann boundary conditions in a smooth bounded domain Ω⊂RnΩ⊂Rn (n≥1n≥1), where χ>0χ>0, the function ψ(u)ψ(u) is the chemotactic sensitivity, g(u)g(u) is the production rate of the chemoattractant and f(u)f(u) is the logistic source. Under some suitable assumptions on the nonlinearities ψ(u)ψ(u), g(u)g(u) and logistic source f(u)f(u), we study the global boundedness of solutions for the problem.