caa a22 4500 606194398 CHVBK 20210128100914.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s00030-015-0325-2 doi (NATIONALLICENCE)springer-10.1007/s00030-015-0325-2 Homogenization of diffusion problems with a nonlinear interfacial resistance [Elektronische Daten] [Patrizia Donato, Kim Le Nguyen] In this paper, we consider a stationary heat problem on a two-component domain with an ε-periodic imperfect interface, on which the heat flux is proportional via a nonlinear function to the jump of the solution, and depends on a real parameter γ. Homogenization and corrector results for the corresponding linear case have been proved in Donato etal. (J Math Sci 176(6):891-927, 2011), by adapting the periodic unfolding method [see (Cioranescu etal. SIAM J Math Anal 40(4):1585-1620, 2008), (Cioranescu etal. SIAM J Math Anal 44(2):718-760, 2012), (Cioranescu etal. Asymptot Anal 53(4):209-235, 2007)] to the case of a two-component domain. Here, we first prove, under natural growth assumptions on the nonlinearities, the existence and the uniqueness of a solution of the problem. Then, we study, using the periodic unfolding method, its asymptotic behavior when $${\varepsilon\to 0}$$ ε → 0 . In order to describe the homogenized problem, we complete some convergence results of Donato etal. (J Math Sci 176(6):891-927, 2011) concerning the unfolding operators and we investigate the limit behaviour of the unfolded Nemytskii operators associated to the nonlinear terms. According to the values of the parameter γ we have different limit problems, for the cases $${\gamma < -1, \gamma =-1}$$ γ < - 1 , γ = - 1 and $${\gamma \in \left] -1,1\right]}$$ γ ∈ - 1 , 1 . The most relevant case is $${\gamma =-1}$$ γ = - 1 , where the homogenized matrix differs from that of the linear case, and is described in a more complicated way, via a nonlinear function involving the correctors. Springer Basel, 2015 Periodic homogenization nationallicence Elliptic equations with jump nationallicence Nonlinear interface conditions nationallicence Donato Patrizia Laboratoire de Mathématiques Raphaël Salem, CNRS UMR 6085, Normandie Université, Université de Rouen, Avenue de l'Université, BP 12, 76801, Saint-Étienne du Rouvray Cedex, France aut Le Nguyen Kim Laboratoire de Mathématiques Raphaël Salem, CNRS UMR 6085, Normandie Université, Université de Rouen, Avenue de l'Université, BP 12, 76801, Saint-Étienne du Rouvray Cedex, France aut Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/5(2015-10-01), 1345-1380 1021-9722 22:5<1345 2015 22 30 https://doi.org/10.1007/s00030-015-0325-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00030-015-0325-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Donato Patrizia Laboratoire de Mathématiques Raphaël Salem, CNRS UMR 6085, Normandie Université, Université de Rouen, Avenue de l'Université, BP 12, 76801, Saint-Étienne du Rouvray Cedex, France aut NATIONALLICENCE 700 1- Le Nguyen Kim Laboratoire de Mathématiques Raphaël Salem, CNRS UMR 6085, Normandie Université, Université de Rouen, Avenue de l'Université, BP 12, 76801, Saint-Étienne du Rouvray Cedex, France aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/5(2015-10-01), 1345-1380 1021-9722 22:5<1345 2015 22 30