Global existence and infinite time blow-up of classical solutions to chemotaxis systems of local sensing in higher dimensions

This paper deals with the fully parabolic chemotaxis system of local sensing in higher dimensions. Despite striking similarity between this and Keller–Segel system, we prove absence finite-time blow-up phenomenon even supercritical case. It means that for any regular initial data, independently magnitude mass, classical solution exists globally time dimensional setting. Moreover, exponential decaying motility case, it is established solutions may blow up at infinite mass. In order to our theorem, deal some auxiliary identity as an evolution equation a dependent operator. view new perspective, direct consequence abstract theory rich enough establish global existence system.