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Keller-Segel Chemotaxis Models: A Review

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Abstract

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.

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Authors thank the referees for constructive comments which have improved the quality of the paper considerably.

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    Gurusamy Arumugam & Jagmohan Tyagi

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Arumugam, G., Tyagi, J. Keller-Segel Chemotaxis Models: A Review. Acta Appl Math 171, 6 (2021). https://doi.org/10.1007/s10440-020-00374-2

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