The one‐dimensional chemotaxis model: global existence and asymptotic profile

Osaki and Yagi (2001) give a proof of global existence for the classical chemotaxis model in one space dimension with use of energy estimates. Here we present an alternative proof which uses the regularity properties of the heat‐equation semigroup. With this method we can identify a large selection of admissible spaces, such that the chemotaxis model defines a global semigroup on these spaces. We use scaling arguments to derive the asymptotic profile of the solutions and we show numerical simulations.