caa a22 4500 605496315 CHVBK 20210128100535.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10231-014-0421-7 doi (NATIONALLICENCE)springer-10.1007/s10231-014-0421-7 Pereira Marcone Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Av. Arlindo Béttio 1000, 03828-000, São Paulo, SP, Brazil aut Parabolic problems in highly oscillating thin domains [Elektronische Daten] [Marcone Pereira] In this work, we consider the asymptotic behavior of the nonlinear semigroup defined by a semilinear parabolic problem with homogeneous Neumann boundary conditions posed in a region of $${\mathbb {R}}^2$$ R 2 that degenerates into a line segment when a positive parameter $$\epsilon $$ ϵ goes to zero (a thin domain). Here we also allow that its boundary presents highly oscillatory behavior with different orders and variable profile. We take thin domains possessing the same order $$\epsilon $$ ϵ to the thickness and amplitude of the oscillations, but assuming different order to the period of oscillations on the top and the bottom of the boundary. Combining methods from linear homogenization theory and the theory on nonlinear dynamics of dissipative systems, we obtain the limit problem establishing convergence properties for the nonlinear semigroup, as well as the upper semicontinuity of the attractors and stationary states. Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 Partial differential equations on infinite-dimensional spaces nationallicence Asymptotic behavior of solutions nationallicence Attractors nationallicence Singular perturbations nationallicence Thin domains nationallicence Oscillatory behavior nationallicence Homogenization nationallicence Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/4(2015-08-01), 1203-1244 0373-3114 194:4<1203 2015 194 10231 https://doi.org/10.1007/s10231-014-0421-7 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/s10231-014-0421-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Pereira Marcone Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Av. Arlindo Béttio 1000, 03828-000, São Paulo, SP, Brazil aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/4(2015-08-01), 1203-1244 0373-3114 194:4<1203 2015 194 10231