Blow-up prevention by logistic source an N-dimensional parabolic-elliptic predator-prey system with indirect pursuit-evasion interaction

Abstract

This paper is concerned with a pursuit-evasion model(1.0){ut=Δu−χ∇⋅(u∇w)+u(λ1−μ1ur1−1+av),x∈Ω,t>0,vt=Δv+ξ∇⋅(v∇z)+v(λ2−μ2vr2−1−bu),x∈Ω,t>0,0=Δw−w+v,x∈Ω,t>0,0=Δz−z+u,x∈Ω,t>0 in a smooth bounded domain Ω⊂RN,N≥1, where χ>0,ξ>0,λi>0,μi>0 and ri>1(i=1,2). For the case r1>1,r2>1, it will be proved that if (r1−1)(r2−1)>(N−2)+N, then for all appropriately regular nonnegative initial data u0 and v0, the problem possesses a unique global-in-time classical solution that is bounded in Ω×(0,∞). This extends the previous global boundedness result for r1=r2=2 and N≤3 (see Li et al. (2020) [12]).