An attraction‐repulsion chemotaxis system with logistic source

This paper deals with the attraction‐repulsion chemotaxis system with logistic source urn:x-wiley:00442267:media:zamm201400311:zamm201400311-math-0001 under homogeneous Neumann boundary conditions in a smooth bounded domain . Under a growth restriction on logistic source and suitable assumptions on the positive parameters χ, ξ, α, β, γ and δ, we show the existence of global bounded classical solutions. The global weak solution is also constructed if the logistic damping effect is rather mild. Furthermore, we obtain the asymptotic behavior of solutions for the logistic source .