Keller-Segel chemotaxis models: a review

Show simple item record Arumugam, Gurusamy Tyagi, Jagmohan
dc.contributor.other Acta Applicandae Mathematicae
dc.coverage.spatial United Kingdom 2021-01-01T15:35:33Z 2021-01-01T15:35:33Z 2021-01
dc.identifier.citation Arumugam, Gurusamy and Tyagi, Jagmohan, "Keller-Segel chemotaxis models: a review", Acta Applicandae Mathematicae, DOI: 10.1007/s10440-020-00374-2, vol. 171, no. 1, Feb. 2021. en_US
dc.identifier.issn 0167-8019
dc.identifier.issn 1572-9036
dc.description.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.
dc.description.statementofresponsibility by Gurusamy Arumugam and Jagmohan Tyagi
dc.format.extent vol. 171, no. 1
dc.language.iso en_US en_US
dc.publisher Springer en_US
dc.subject Chemotaxis en_US
dc.subject Keller-Segel models en_US
dc.subject Weak solutions en_US
dc.subject Renormalized solutions en_US
dc.subject Local existence en_US
dc.subject Global existence en_US
dc.subject Blow-up en_US
dc.subject Boundedness en_US
dc.subject Stabilization en_US
dc.subject Asymptotic behavior of solutions en_US
dc.subject Finite difference method en_US
dc.subject Finite element method en_US
dc.subject Finite Volume method en_US
dc.subject Discontinuous Galerkin method en_US
dc.title Keller-Segel chemotaxis models: a review en_US
dc.type Article en_US

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