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- W2885874796 abstract "This paper deals with positive solutions of the fully parabolic system{ut=Δu−χ∇⋅(u∇v)inΩ×(0,∞),τ1vt=Δv−v+winΩ×(0,∞),τ2wt=Δw−w+uinΩ×(0,∞) under mixed boundary conditions (no-flux and Dirichlet conditions) in a smooth bounded convex domain Ω⊂R4 with positive parameters τ1,τ2,χ>0 and nonnegative smooth initial data (u0,v0,w0). Global existence and boundedness of solutions were shown if ‖u0‖L1(Ω)<(8π)2/χ in Fujie–Senba (2017). In the present paper, it is shown that there exist blowup solutions satisfying ‖u0‖L1(Ω)>(8π)2/χ. This result suggests that the system can be regard as a generalization of the Keller–Segel system, which has 8π/χ-dichotomy. The key ingredients are a Lyapunov functional and quantization properties of stationary solutions of the system in R4." @default.
- W2885874796 created "2018-08-22" @default.
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- W2885874796 date "2019-01-01" @default.
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- W2885874796 title "Blowup of solutions to a two-chemical substances chemotaxis system in the critical dimension" @default.
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- W2885874796 doi "https://doi.org/10.1016/j.jde.2018.07.068" @default.
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