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A multi-species chemotaxis system: Lyapunov functionals, duality, critical mass
Kavallaris, Nikos I. Ricciardi, Tonia Zecca, Gabriela
Kavallaris, Nikos I.
Ricciardi, Tonia
Zecca, Gabriela
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2017-10-09
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Abstract
We introduce a multi-species chemotaxis type system admitting an arbitrarily large number of population species, all of which are attracted vs.\ repelled by a single chemical substance. The production vs.\ destruction rates of the chemotactic substance by the species is described by a probability measure. For such a model we investigate the variational structures, in particular we prove the existence of Lyapunov functionals, we establish duality properties as well as a logarithmic Hardy-Littlewood-Sobolev type inequality for the associated free energy.
The latter inequality provides the optimal critical value for the conserved total population mass.
Citation
Kavallaris, N. I., Ricciardi, T., & Zecca, G. (2018). A multi-species chemotaxis system: Lyapunov functionals, duality, critical mass. European Journal of Applied Mathematics, 29(3), 515-542. http://doi.org/10.1017/S0956792517000286
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Cambridge University Press
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European Journal of Applied Mathematics
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Article
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en
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This article has been accepted for publication and will appear in a revised form, subsequent to peer review and/or editorial input by Cambridge University Press, in European Journal of Applied Mathematics published by Cambridge University Press. Copyright Cambridge University Press 2017.
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1469-4425