{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:46:16Z","timestamp":1760147176091,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,15]],"date-time":"2023-01-15T00:00:00Z","timestamp":1673740800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004569","name":"Ministry of Science and Higher Education","doi-asserted-by":"publisher","award":["122082400001-8"],"award-info":[{"award-number":["122082400001-8"]}],"id":[{"id":"10.13039\/501100004569","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The paper is devoted to the theoretical analysis and numerical implementation of a mathematical model of a nonlinear reaction\u2013diffusion system on the COMSOL Multiphysics platform. The applied problem of the computer simulation of polarization switching in thin ferroelectric films is considered. The model is based on the Landau\u2013Ginzburg\u2013Devonshire\u2013Khalatnikov thermodynamic approach and formalized as an initial-boundary value problem for a semilinear parabolic partial differential equation. The theoretical foundations of the model were explained. The user interface design application was developed with COMSOL Multiphysics. A series of computational experiments was performed to study the ferroelectric hysteresis and temperature dependences of polarization on the example of a ferroelectric barium titanate film.<\/jats:p>","DOI":"10.3390\/computation11010014","type":"journal-article","created":{"date-parts":[[2023,1,16]],"date-time":"2023-01-16T01:31:15Z","timestamp":1673832675000},"page":"14","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Size-Dependent Switching in Thin Ferroelectric Films: Mathematical Aspects and Finite Element Simulation"],"prefix":"10.3390","volume":"11","author":[{"given":"Elena","family":"Veselova","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, Amur State University, Ignatyevskoye Shosse, 21, Amur Region, 675027 Blagoveshchensk, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5628-3519","authenticated-orcid":false,"given":"Anna","family":"Maslovskaya","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Amur State University, Ignatyevskoye Shosse, 21, Amur Region, 675027 Blagoveshchensk, Russia"}]},{"given":"Alexander","family":"Chebotarev","sequence":"additional","affiliation":[{"name":"Institute for Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences, Radio St., 7, 690041 Vladivostok, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,15]]},"reference":[{"key":"ref_1","unstructured":"Otten, D. 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