Pattern Formation (i): the Keller-segel Model
نویسندگان
چکیده
Abstract. We investigate nonlinear dynamics near an unstable constant equilibrium in the classical Keller-Segel model. Given any general perturbation of magnitude δ, we prove that its nonlinear evolution is dominated by the corresponding linear dynamics along a fixed finite number of fastest growing modes, over a time period of ln 1 δ . Our result can be interpreted as a rigourous mathematical characterization for early pattern formation in the Keller-Segel model.
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