Pattern Formation of a Keller-Segel Model with the Source Term up(1-u)‎

Abstract EN

Nonlinear dynamics near an unstable constant equilibrium in a Keller-Segel model with the source term up(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/δ), where δ is a strength of the initial perturbation.