Pattern formation. I: The Keller-Segel model (Q1958435)

This paper concerns the nonlinear dynamics near an unstable constant equilibrium in the classical Keller-Segel model. The authors have proved that for any perturbation of magnitude \(\delta \), the nonlinear evolution is dominated by the corresponding linear dynamics along a fixed finite number of fastest growing modes, over a time period of \(\ln \frac{1}{\delta }\). The main results represents a rigorous mathematical characterization for early pattern formation in the Keller-Segel model.