LAUSR

Abstract This paper is concerned with the two-species chemotaxis system { u t = △ u − ∇ ⋅ ( u χ 1 ( w ) ∇ w ) + μ 1 u ( 1 − u − a 1 v ) , x ∈ Ω , t > 0 , v t = △ v − ∇ ⋅ ( v χ 2 ( w ) ∇ w ) + μ 2 v ( 1 − a 2 u − v ) , x ∈ Ω , t > 0 , w t = d Δ w − w + u + v , x ∈ Ω , t > 0 in a bounded smooth domain Ω ⊂ R n ( n ≥ 1 ) , where d > 0 , μ i ≥ 0 and a i ≥ 0 ( i = 1 , 2 ) are parameters, χ i are functions satisfying some conditions. The purpose of this paper is to show the global boundedness of solutions to the above system under weaker conditions than those assumed in the related literature.