--- _id: '10878' abstract: - lang: eng text: Starting from a microscopic model for a system of neurons evolving in time which individually follow a stochastic integrate-and-fire type model, we study a mean-field limit of the system. Our model is described by a system of SDEs with discontinuous coefficients for the action potential of each neuron and takes into account the (random) spatial configuration of neurons allowing the interaction to depend on it. In the limit as the number of particles tends to infinity, we obtain a nonlinear Fokker-Planck type PDE in two variables, with derivatives only with respect to one variable and discontinuous coefficients. We also study strong well-posedness of the system of SDEs and prove the existence and uniqueness of a weak measure-valued solution to the PDE, obtained as the limit of the laws of the empirical measures for the system of particles. acknowledgement: "The second author has been partially supported by INdAM through the GNAMPA Research\r\nProject (2017) “Sistemi stocastici singolari: buona posizione e problemi di controllo”. The third\r\nauthor was partly funded by the Austrian Science Fund (FWF) project F 65." article_processing_charge: No article_type: original author: - first_name: Franco full_name: Flandoli, Franco last_name: Flandoli - first_name: Enrico full_name: Priola, Enrico last_name: Priola - first_name: Giovanni A full_name: Zanco, Giovanni A id: 47491882-F248-11E8-B48F-1D18A9856A87 last_name: Zanco citation: ama: Flandoli F, Priola E, Zanco GA. A mean-field model with discontinuous coefficients for neurons with spatial interaction. Discrete and Continuous Dynamical Systems. 2019;39(6):3037-3067. doi:10.3934/dcds.2019126 apa: Flandoli, F., Priola, E., & Zanco, G. A. (2019). A mean-field model with discontinuous coefficients for neurons with spatial interaction. Discrete and Continuous Dynamical Systems. American Institute of Mathematical Sciences. https://doi.org/10.3934/dcds.2019126 chicago: Flandoli, Franco, Enrico Priola, and Giovanni A Zanco. “A Mean-Field Model with Discontinuous Coefficients for Neurons with Spatial Interaction.” Discrete and Continuous Dynamical Systems. American Institute of Mathematical Sciences, 2019. https://doi.org/10.3934/dcds.2019126. ieee: F. Flandoli, E. Priola, and G. A. Zanco, “A mean-field model with discontinuous coefficients for neurons with spatial interaction,” Discrete and Continuous Dynamical Systems, vol. 39, no. 6. American Institute of Mathematical Sciences, pp. 3037–3067, 2019. ista: Flandoli F, Priola E, Zanco GA. 2019. A mean-field model with discontinuous coefficients for neurons with spatial interaction. Discrete and Continuous Dynamical Systems. 39(6), 3037–3067. mla: Flandoli, Franco, et al. “A Mean-Field Model with Discontinuous Coefficients for Neurons with Spatial Interaction.” Discrete and Continuous Dynamical Systems, vol. 39, no. 6, American Institute of Mathematical Sciences, 2019, pp. 3037–67, doi:10.3934/dcds.2019126. short: F. Flandoli, E. Priola, G.A. Zanco, Discrete and Continuous Dynamical Systems 39 (2019) 3037–3067. date_created: 2022-03-18T12:33:34Z date_published: 2019-06-01T00:00:00Z date_updated: 2023-09-08T11:34:45Z day: '01' department: - _id: JaMa doi: 10.3934/dcds.2019126 external_id: arxiv: - '1708.04156' isi: - '000459954800003' intvolume: ' 39' isi: 1 issue: '6' keyword: - Applied Mathematics - Discrete Mathematics and Combinatorics - Analysis language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1708.04156 month: '06' oa: 1 oa_version: Preprint page: 3037-3067 project: - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems publication: Discrete and Continuous Dynamical Systems publication_identifier: issn: - 1553-5231 publication_status: published publisher: American Institute of Mathematical Sciences quality_controlled: '1' scopus_import: '1' status: public title: A mean-field model with discontinuous coefficients for neurons with spatial interaction type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 39 year: '2019' ...