Systems of partial differential equations and nonlinear elliptic equations
Applications of pseudo-differential methods to boundary value problems
Well-posedness and qualitative properties for nonlinear PDEs
| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Sao Paulo, Inst Matemat & Estat, Dept Matemat Aplicada, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil
Total Affiliations: 1
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| Document type: | Journal article |
| Source: | Journal of Mathematical Analysis and Applications; v. 441, n. 1, p. 375-392, SEP 1 2016. |
| Web of Science Citations: | 5 |
| Abstract | |
In this paper we analyze the behavior of a family of steady state solutions of a semilinear reaction diffusion equation with homogeneous Neumann boundary condition, posed in a two-dimensional thin domain with reaction terms concentrated in a narrow oscillating neighborhood of the boundary. We assume that the domain, and therefore, the oscillating boundary neighborhood, degenerates into an interval as a small parameter epsilon goes to zero. Our main result is that this family of solutions converges to the solution of a one-dimensional limit equation capturing the geometry and oscillatory behavior of the open sets where the problem is established. (C) 2016 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 13/22275-1 - Dynamical systems given by semilinear parabolic equations |
| Grantee: | Marcone Corrêa Pereira |
| Support Opportunities: | Regular Research Grants |