| Full text | |
| Author(s): |
de Araujo, Patricia Neves
;
Nakasato, Jean Carlos
;
Pereira, Marcone Correa
Total Authors: 3
|
| Document type: | Journal article |
| Source: | REVISTA MATEMATICA COMPLUTENSE; v. N/A, p. 41-pg., 2025-10-03. |
| Abstract | |
In this paper, we investigate the behavior of the solutions of a semilinear elliptic equation posed in a thin domain with an outward peak. Such peak is given by a nonnegative function which sets the profile of our region and makes the analysis challenging. In a first moment, we apply standard methods from asymptotic analysis and thin domains to show the strong convergence of the solutions of the linear version of the problem also determining the rate of convergence. In the sequel, we derive conditions under which the linear limit equation has a compact resolvent in order to analyze the semilinear equation. We obtain upper and lower semicontinuity of the solutions establishing rate of convergence under appropriated conditions on the geometry of the thin domain. (AU) | |
| FAPESP's process: | 22/08112-1 - Boundary perturbation problems on partial differential equations |
| Grantee: | Jean Carlos Nakasato |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 20/14075-6 - Dynamical systems and their attractors under perturbations |
| Grantee: | Alexandre Nolasco de Carvalho |
| Support Opportunities: | Research Projects - Thematic Grants |