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- W4320175774 abstract "This paper is concerned with the following parabolic-parabolic-elliptic chemotaxis system with singular sensitivity and Lotka-Volterra competitive kinetics,(0.1){ut=Δu−χ1∇⋅(uw∇w)+u(a1−b1u−c1v),x∈Ωvt=Δv−χ2∇⋅(vw∇w)+v(a2−b2v−c2u),x∈Ω0=Δw−μw+νu+λv,x∈Ω∂u∂n=∂v∂n=∂w∂n=0,x∈∂Ω, where Ω⊂RN is a bounded smooth domain, and χi, ai, bi, ci (i=1,2) and μ,ν,λ are positive constants. This is the first work on two-species chemotaxis-competition system with singular sensitivity and Lotka-Volterra competitive kinetics. Among others, we prove that for any given nonnegative initial data u0,v0∈C0(Ω¯) with u0+v0≢0, (0.1) has a unique globally defined classical solution (u(t,x;u0,v0),v(t,x;u0,v0),w(t,x;u0,v0)) with u(0,x;u0,v0)=u0(x) and v(0,x;u0,v0)=v0(x) in any space dimensional setting with any positive constants χi,ai,bi,ci (i=1,2) and μ,ν,λ. Moreover, we prove that there is χ⁎(μ,χ1,χ2)>0 satisfyingχ⁎(μ,χ1,χ2)={μχ24if0<χ<2μ(χ−1)ifχ≥2,whenχ1=χ2:=χandχ⁎(μ,χ1,χ2)≤min{μχ2+μ(χ1−χ2)24,μχ1+μ(χ2−χ1)24},whenχ1≠χ2 such that the conditionmin{a1,a2}>χ⁎(μ,χ1,χ2) implieslimsupt→∞‖u(t,⋅;u0,v0)+v(t,⋅;u0,v0)‖∞≤M⁎andliminft→∞infx∈Ω(u(t,x,u0,v0)+v(t,x;u0,v0))≥m⁎ for some positive constants M⁎,m⁎ independent of u0,v0, the latter is referred to as combined pointwise persistence." @default.
- W4320175774 created "2023-02-13" @default.
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- W4320175774 date "2023-05-01" @default.
- W4320175774 modified "2023-10-14" @default.
- W4320175774 title "Two-species chemotaxis-competition system with singular sensitivity: Global existence, boundedness, and persistence" @default.
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- W4320175774 doi "https://doi.org/10.1016/j.jde.2023.01.029" @default.
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