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Pattern formation (I): The Keller-Segel Model

Yan Guo·Hyung Ju Hwang
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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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Yan Guo, Hyung Ju Hwang. 2005-09-14. Pattern formation (I): The Keller-Segel Model. https://arxiv.org/abs/math/0509305

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