Boundedness and Asymptotic Behavior to a Chemotaxis System with Indirect Signal Generation and Singular Sensitivity

Abstract

In this paper, we consider the following indirect signal generation and singular sensitivity nt=Δn+χ∇⋅n/ϕc∇c, x∈Ω,t>0,ct=Δc-c+w, x∈Ω,t>0,wt=Δw-w+n, x∈Ω,t>0, in a bounded domain Ω⊂RNN=2,3 with smooth boundary ∂Ω. Under the nonflux boundary conditions for n, c, and w, we first eliminate the singularity of ϕc by using the Neumann heat semigroup and then establish the global boundedness and rates of convergence for solution.