Pattern formation of a Keller-Segel model with the source term \(u^p(1 - u)\) (Q2337042)

Summary: Nonlinear dynamics near an unstable constant equilibrium in a Keller-Segel model with the source term \(u^p(1 - u)\) is considered. It is proved that nonlinear dynamics of a general perturbation is determined by the finite number of linear growing modes over a time scale of \(\ln(1 / \delta)\), where \(\delta\) is a strength of the initial perturbation.