Collective behavior models with vision geometrical constraints: Truncated noises and propagation of chaos

Young Pil Choi, Samir Salem

Research output: Contribution to journalArticlepeer-review

Abstract

We consider large systems of stochastic interacting particles through discontinuous kernels which has vision geometrical constrains. We rigorously derive a Vlasov–Fokker–Planck type of kinetic mean-field equation from the corresponding stochastic integral inclusion system. More specifically, we construct a global-in-time weak solution to the stochastic integral inclusion system and derive the kinetic equation with the discontinuous kernels and the inhomogeneous noise strength by employing the 1-Wasserstein distance.

Original languageEnglish
Pages (from-to)6109-6148
Number of pages40
JournalJournal of Differential Equations
Volume266
Issue number9
DOIs
Publication statusPublished - 2019 Apr 15

Bibliographical note

Funding Information:
The authors warmly thank Professor Maxime Hauray for helpful discussion and valuable comments. YPC was supported by NRF grant (no. 2017R1C1B2012918 and 2017R1A4A1014735) and POSCO Science Fellowship of POSCO TJ Park Foundation. SS was supported by the Fondation des Sciences Math?matiques de Paris and Universit? Paris Sciences et Lettres.

Funding Information:
The authors warmly thank Professor Maxime Hauray for helpful discussion and valuable comments. YPC was supported by NRF grant (no. 2017R1C1B2012918 and 2017R1A4A1014735 ) and POSCO Science Fellowship of POSCO TJ Park Foundation . SS was supported by the Fondation des Sciences Mathématiques de Paris and Université Paris Sciences et Lettres .

Funding Information:
The authors warmly thank Professor Maxime Hauray for helpful discussion and valuable comments. YPC was supported by NRF grant (no. 2017R1C1B2012918 and 2017R1A4A1014735) and POSCO Science Fellowship of POSCO TJ Park Foundation. SS was supported by the Fondation des Sciences Mathématiques de Paris and Université Paris Sciences et Lettres.

Publisher Copyright:
© 2018 Elsevier Inc.

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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