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

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

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