摘要：
This work explores the predator-prey chemotaxis system with two chemicals {u_(t) = Δu + ∇ ・ (u∇v) + μ_(1)u(1 − u − α_(1)w), x ∈ Ω, t > 0,v_(t )= Δv −α_(1)v + β_(1)w, x ∈ Ω, t > 0,w_(t) = Δw − ξ∇ ・ (w∇z) + μ_(2)w(1 + α_(2)u − w), x ∈ Ω, t > 0,z_(t) =Δz −α_(2)z +β_(2)u, x ∈ Ω, t > 0, in an arbitrary smooth bounded domainΩ■R^(n) under homogeneous Neumann boundary conditions.The parameters in the system are positive.We first prove that if n≤3,the corresponding initial-boundary value problem admits a unique global bounded classical solution,under the assumption thatχ,ξ,μ_(i),a_(i),α_(i) andβ_(i)(i=1,2)satisfy some suitable conditions.Subsequently,we also analyse the asymptotic behavior of solutions to the above system and show that·when a_(1)1 andμ_(2)/ξ_(2) is sufficiently large,the global bounded classical solution(u,v,w,z)of this system exponentially converges to(0,α_(1)/β_(1),1,0)as t→∞;·when a1=1 andμ_(2)/ξ_(2) is sufficiently large,the global bounded classical solution(u,v,w,z)of this system polynomially converges to(0,α_(1)/β_(1),1,0)as t→∞.
