| Full text | |
| Author(s): |
Pereira, Marcone C.
[1]
Total Authors: 1
|
| Affiliation: | [1] Univ Sao Paulo, Escola Artes Ciencias & Humanidades, BR-03828000 Sao Paulo, SP - Brazil
Total Affiliations: 1
|
| Document type: | Journal article |
| Source: | Annali di Matematica Pura ed Applicata; v. 194, n. 4, p. 1203-1244, AUG 2015. |
| Web of Science Citations: | 5 |
| Abstract | |
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 R-2 that degenerates into a line segment when a positive parameter epsilon 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 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. (AU) | |
| FAPESP's process: | 13/22275-1 - Dynamical systems given by semilinear parabolic equations |
| Grantee: | Marcone Corrêa Pereira |
| Support Opportunities: | Regular Research Grants |