Study of two-species chemotaxis models

Abstract : This thesis is concerned about cellular motion of a population composed of two species in interaction through chemical cues. The chemical cues to which the two species are subject are of different kind.They can be internal (produced by the two species) or external (present in the meduim and consommed by the two species). Synchronising and non-synchronising effects are observed during the migration of the population formed by two different strains of E.Coli.Although separately, red bacteria E.Coli travel twice as fast as green bacteria E.Coli, put together, they travel or split depending on the percentage of the faster bacteria in the population. This experimental result is explained by a two-species parabolic macroscopic chemotaxis model for which the existence and non-existence of traveling pulses are showed. The parabolic macroscopic model is derived from microscopic models which describe the individual motion of cells. The synchronising and non-synchronising effect is also encountered in dynamics of the two-species dirac masses after blow-up of classical solutions in a two-species model for aggregation. A method to design both well-balanced and asymptotic preserving schemes is proposed. This method is tested to chemotaxis and radiative transport kinetic models.
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Casimir Emako Kazianou. Study of two-species chemotaxis models. General Mathematics [math.GM]. Université Pierre et Marie Curie - Paris VI, 2016. English. ⟨NNT : 2016PA066045⟩. ⟨tel-01365414⟩

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