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• W2801239675 abstract "This paper deals with a Neumann boundary value problem in a d-dimensional box $mathbb{T}^{d}=(0,pi)^{d}$ ( $d=1, 2, 3$ ) for a nonlinear diffusion chemotaxis model with logistic source. By using the embedding theorem, the higher-order energy estimates and bootstrap arguments, the condition of chemotaxis-driven instability and the nonlinear evolution near an unstable positive constant equilibrium for this chemotaxis model are proved. Our result provides a quantitative characterization for early spatial pattern formation on the positive constant equilibrium. Finally, numerical simulations are carried out to support our theoretical nonlinear instability results." @default.
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• W2801239675 date "2018-04-20" @default.
• W2801239675 modified "2023-09-28" @default.
• W2801239675 title "Pattern formation for a nonlinear diffusion chemotaxis model with logistic source" @default.
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• W2801239675 doi "https://doi.org/10.1186/s13661-018-0976-0" @default.
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