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 language | English |
|---|---|
| Pages (from-to) | 121-161 |
| Number of pages | 41 |
| Journal | Journal of the European Mathematical Society |
| Volume | 21 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2019 Jan 1 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics
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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 journal › Article
TY - JOUR
T1 - Mean-field limit for collective behavior models with sharp sensitivity regions
AU - Carrillo, José A.
AU - Choi, Young Pil
AU - Hauray, Maxime
AU - Salem, Samir
PY - 2019/1/1
Y1 - 2019/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85056178579&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85056178579&partnerID=8YFLogxK
U2 - 10.4171/JEMS/832
DO - 10.4171/JEMS/832
M3 - Article
AN - SCOPUS:85056178579
VL - 21
SP - 121
EP - 161
JO - Journal of the European Mathematical Society
JF - Journal of the European Mathematical Society
SN - 1435-9855
IS - 1
ER -