Mean-field limit for collective behavior models with sharp sensitivity regions

José A. Carrillo, Young Pil Choi, Maxime Hauray, Samir Salem

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We rigorously show the mean-field limit for a large class of swarming individual based models with local sharp sensitivity regions. For instance, these models include nonlocal repulsive-attractive forces locally averaged over sharp vision cones and Cucker–Smale interactions with discontinuous communication weights. We define global-in-time solutions through a differential inclusion system corresponding to the particle descriptions. We estimate the error between the solutions to the differential inclusion system and weak solutions to the expected limiting kinetic equation by employing tools from optimal transport theory. Quantitative bounds on the expansion of the 1-Wasserstein distance along flows based on a weak-strong stability estimate are obtained. We also provide various examples of realistic sensitivity sets satisfying the assumptions of our main results.

Original languageEnglish
Pages (from-to)121-161
Number of pages41
JournalJournal of the European Mathematical Society
Volume21
Issue number1
DOIs
Publication statusPublished - 2019 Jan 1

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Mean-field Limit
Collective Behavior
Differential Inclusions
Limiting Equations
Wasserstein Distance
Individual-based Model
Optimal Transport
Strong Stability
Transport Theory
Stability Estimates
Kinetic Equation
Weak Solution
Cones
Cone
Kinetics
Communication
Interaction
Model
Estimate
Vision

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Carrillo, José A. ; Choi, Young Pil ; Hauray, Maxime ; Salem, Samir. / Mean-field limit for collective behavior models with sharp sensitivity regions. In: Journal of the European Mathematical Society. 2019 ; Vol. 21, No. 1. pp. 121-161.
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Mean-field limit for collective behavior models with sharp sensitivity regions. / Carrillo, José A.; Choi, Young Pil; Hauray, Maxime; Salem, Samir.

In: Journal of the European Mathematical Society, Vol. 21, No. 1, 01.01.2019, p. 121-161.

Research output: Contribution to journalArticle

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