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We show the convergence of solutions towards those of the homogenized problems depending on the relations between the parameters distance, sizes, and reaction.<\/jats:p>","DOI":"10.3846\/mma.2024.20137","type":"journal-article","created":{"date-parts":[[2024,11,22]],"date-time":"2024-11-22T12:12:27Z","timestamp":1732277547000},"page":"694-713","update-policy":"https:\/\/doi.org\/10.3846\/mma_policy","source":"Crossref","is-referenced-by-count":2,"title":["Averaged reaction for nonlinear boundary conditions on a grill-type Winkler foundation"],"prefix":"10.3846","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8791-7684","authenticated-orcid":true,"given":"Delfina","family":"G\u00f3mez","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Estad\u00edstica y Computaci\u00f3n, Universidad de Cantabria, Av. Los Castros s.n., 39005 Santander, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7863-0043","authenticated-orcid":true,"given":"Mar\u00eda-Eugenia","family":"P\u00e9rez-Mart\u00ednez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada y Ciencias de la Computaci\u00f3n, Universidad de Cantabria, Av. Los Castros s.n., 39005 Santander, Spain"}]}],"member":"2209","published-online":{"date-parts":[[2024,11,22]]},"reference":[{"doi-asserted-by":"publisher","unstructured":"A. Brillard, M. Lobo and E. P\u00e9rez. Homog\u00e9n\u00e9isation de fronti\u00e8res par epiconvergence en \u00e9lasticit\u00e9 lin\u00e9are. RAIRO Mod\u00e9l. Math. Anal. Num\u00e9r., 24(1):5-26, 1990. https:\/\/doi.org\/10.1051\/m2an\/1990240100051","key":"10.3846\/mma.2024.20137-0","DOI":"10.1051\/m2an\/1990240100051"},{"doi-asserted-by":"publisher","unstructured":"M. Dalla Riva, G. Mishuris and P. Musolino. A degenerating Robin-type traction problem in a periodic domain. Math. 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Shaposhnikova and M.N. Zubova. On critical parameters in homogenization of perforated domains by thin tubes with nonlinear flux and related spectral problems. Math. Methods Appl. Sci., 38(12):2606- 2629, 2015. https:\/\/doi.org\/10.1002\/mma.3246","key":"10.3846\/mma.2024.20137-4","DOI":"10.1002\/mma.3246"},{"doi-asserted-by":"publisher","unstructured":"D. G\u00f3mez, S.A. Nazarov and E. P\u00e9rez. Homogenization of Winkler-Steklov spectral conditions in three-dimensional linear elasticity. Z. Angew. Math. Phys, 69(2):35, 2018. https:\/\/doi.org\/10.1007\/s00033-018-0927-8","key":"10.3846\/mma.2024.20137-5","DOI":"10.1007\/s00033-018-0927-8"},{"doi-asserted-by":"publisher","unstructured":"D. G\u00f3mez, S.A Nazarov and M.-E. P\u00e9rez-Mart\u00ednez. Asymptotics for spectral problems with rapidly alternating boundary conditions on a strainer Winkler foundation. J. 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Published by Vilnius Gediminas Technical University","order":0,"name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}