Global classical solutions of a nonlinear consumption system with singular density-suppressed motility

Abstract

In this note, we study the no-flux initial-boundary value problem for the migration-consumption taxis system involving singular density-suppressed motility (⋆)ut=Δ((u+1)lϕ(v)),vt=Δv−uvmin a bounded smooth domain Ω⊂Rn(n⩾2), where ϕ generalizes the singular prototype given by ϕ(ξ)=ξ−α(ξ>0) with α>0. We prove that if l>n2 and m⩾1, then the model (⋆) possesses a global classical solution.