Global existence and boundedness in a fully parabolic attraction-repulsion chemotaxis system with signal-dependent sensitivities and logistic source

This paper deals with the fully parabolic attraction-repulsion chemotaxis system with signal-dependent sensitivities and logistic source, {u_t=Δu−∇⋅(uχ(v)∇v)+∇⋅(uξ(w)∇w)+μu(1−u),x∈Ω,t>0,v_t=Δv−v+u,x∈Ω,t>0,w_t=Δw−w+u,x∈Ω,t>0 under homogeneous Neumann boundary conditions and initial conditions, where Ω⊂Rⁿ (n≥2) is a bounded domain with smooth boundary, χ,ξ are functions satisfying some conditions and μ>0 is a constant. When χ,ξ are constants, it is known that the above system possesses a globally bounded classical solution in some cases. However, there has been no work in the case that χ,ξ are functions. This paper develops global existence and boundedness of classical solutions to the above system in such case.