文摘
This paper considers the attraction–repulsion chemotaxis system: e9cdd5bb6211d51fec1b2435f86ff550" title="Click to view the MathML source">ut=Δu−χ∇⋅(u∇v)+ξ∇⋅(u∇w), 0=Δv+αu−βv, e486e207a" title="Click to view the MathML source">0=Δw+γu−δw, subject to the non-flux boundary condition in a smooth bounded domain Ω⊂R2, with be2b996f69f311a61a2983b82" title="Click to view the MathML source">χ,ξ≥0, bec769d1806b0eb80617a1cdee8a6f9" title="Click to view the MathML source">α,β,γ,δ>0. We establish the finite time blow-up conditions for nonradial solutions that the finite time blow-up occurs at x0∈Ω whenever ∫Ωu0(x)dx>8π/(χα−ξγ) with 99440d3d46a1e7a22a95b5" title="Click to view the MathML source">χα−ξγ>0, under be7e6" 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 994532203f7ea4f42f9ef5863450" title="Click to view the MathML source">δ−β.