Singular solutions of partial differential equations modelling chemotactic aggregation

Abstract

This paper reviews several mathematical results for partial differential equations modelling chemotaxis. In particular, questions like singularity formation for the Keller–Segel model and continuation of the solutions beyond the blow-up time will be discussed. Some of the open problems that remain for the Keller–Segel model as well as some new mathematical problems arising in the study of chemotaxis problems will be discussed.