Global existence for a class of chemotaxis-consumption systems with signal-dependent motility and generalized logistic source

Abstract

In this paper, we study a chemotaxis-consumption system with signal-dependent motility and generalized logistic source in a smooth bounded domain. We show that if α>0, ρ∈R, μ>0 and l>maxn+22,2, then for all sufficiently smooth initial data the system ut=Δ(uv−α)+ρu−μul,x∈Ω,t>0,vt=Δv−uv,x∈Ω,t>0,possesses a unique global-in-time solution.