A multi-species chemotaxis system: Lyapunov functionals, duality, critical mass
2017 ◽
Vol 29
(3)
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pp. 515-542
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Keyword(s):
We introduce a multi-species chemotaxis type system admitting an arbitrarily large number of population species, all of which are attracted versus repelled by a single chemical substance. The production versus 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.
2007 ◽
Vol 2
◽
pp. 423-429
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2007 ◽
Vol 38
(3)
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pp. 437-454
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Keyword(s):
2020 ◽
Vol 268
(10)
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pp. 5996-6032
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Keyword(s):
2004 ◽
Vol 134
(3)
◽
pp. 449-476
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Keyword(s):
Keyword(s):
1998 ◽
Vol 145
(2)
◽
pp. 161-195
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Keyword(s):