文摘
This paper considers the attraction–repulsion chemotaxis system: ut=Δu−χ∇⋅(u∇v)+ξ∇⋅(u∇w), 8554605c30e8741b05c3d9628a419" title="Click to view the MathML source">0=Δv+αu−βv, a4c273d5903e486e207a" title="Click to view the MathML source">0=Δw+γu−δw, subject to the non-flux boundary condition in a smooth bounded domain a4751a3cb085d0e04a3806f24b0cc44" title="Click to view the MathML source">Ω⊂R2, with 9f311a61a2983b82" title="Click to view the MathML source">χ,ξ≥0, α,β,γ,δ>0. We establish the finite time blow-up conditions for nonradial solutions that the finite time blow-up occurs at bf74e3ea631e0c1d6bbdde889ca1" title="Click to view the MathML source">x0∈Ω whenever e7815fd945f857db081e0141b4d3ed4" title="Click to view the MathML source">∫Ωu0(x)dx>8π/(χα−ξγ) with e7a22a95b5" title="Click to view the MathML source">χα−ξγ>0, under bf9ef47b4cdd9f021edbe7e6" title="Click to view the MathML source">∫Ωu0(x)|x−x0|2dx sufficiently small. This does agree with the known blow-up conditions for radial solutions of the same model. The previous blow-up conditions for nonradial solutions are more complicated involving a classification to the sign of e7994532203f7ea4f42f9ef5863450" title="Click to view the MathML source">δ−β.