Global solutions for a path-dependent hybrid system of differential equations under parabolic signal

Menci, Marta; Papi, Marco

doi:10.1016/j.na.2019.01.034

Cited by 9 publications

(3 citation statements)

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“…It is straightforward to adapt the proofs to the case of a general γ satisfying the hypothesis of the present paper. This situation is anyway fully included in [31,Theorem 6] and we have the following result. Theorem 8.1.…”

Section: Hydrodynamic Limitmentioning

confidence: 83%

“…Theorem 2.1. Let ρ in be a compactly supported probability on R 2dN , let Φ t N be the mapping generated by the particles system (3,4,5,6) as defined by (7), and let τ be the function defined in (31).…”

Section: The Main Resultsmentioning

confidence: 99%

“…For this simple model in [13] a full analytical theory was developed in the two-dimensional case with a fixed but arbitrary number N of particles, and results of globally in time existence and uniqueness of solutions were proved, as well as the time-asymptotic linear stability. Other analytical results, for more general hybrid models, can be found in [31].…”

Section: Introductionmentioning

confidence: 99%

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

Natalini,

Paul

2021

Preprint

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In 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 meanfield 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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Section: Hydrodynamic Limitmentioning

confidence: 83%