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The Mean-Field limit for hybrid models of collective motions with chemotaxis

Abstract : IIn this paper we study a general class of hybrid mathematical models of collective motions of cells under the influence of chemical stimuli. The models are hybrid in the sense that cells are discrete entities given by ODE, while the chemoattractant is considered as a continuous signal which solves a diffusive equation. For this model we prove the mean-field limit in the Wasserstein distance to a system given by the coupling of a Vlasov-type equation with the chemoattractant equation. Our approach is not based on empirical measures and we show the limit with explicit bounds, by proving also existence and uniqueness for the limit system. In the monokinetic case we derive pressureless nonlocal Euler-type model with chemotaxis.
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https://hal.archives-ouvertes.fr/hal-03310547
Contributor : Thierry Paul <>
Submitted on : Friday, July 30, 2021 - 3:21:06 PM
Last modification on : Saturday, July 31, 2021 - 3:56:16 AM

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  • HAL Id : hal-03310547, version 1
  • ARXIV : 2107.14645

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Roberto Natalini, Thierry Paul. The Mean-Field limit for hybrid models of collective motions with chemotaxis. 2021. ⟨hal-03310547⟩

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