Receptor

Mathematics

Domain (mathematical analysis)

Chemotaxis

Biology

Partial differential equation

Mathematical analysis

Chemistry

Parabolic partial differential equation

Ecology

Type (biology)

Applied mathematics

Biochemistry

Acta Applicandae Mathematicae

We recount and discuss some of the most important methods and blow-up criteria for analyzing solutions of Keller-Segel chemotaxis models. First, we discuss the results concerning the global existence, boundedness and blow-up of solutions to parabolic-elliptic type models. Thereafter we describe the global existence, boundedness and blow-up of solutions to parabolic-parabolic models. The numerical analysis of these models is still at a rather early stage only. We recollect quite a few of the known results on numerical methods also and direct the attention to a number of open problems in this domain.

Keller-Segel Chemotaxis Models: A Review