NONLINEAR ELLIPTIC EQUATIONS WITH CONCENTRATING REACTION TERMS AT AN OSCILLATORY BOUNDARY

Autor(es)

Arrieta, Jose M. ; Nogueira, Ariadne ; Pereira, Marcone C.

• Tipo de documento: Artigo Científico
• Fonte: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B; v. 24, n. 8, p. 30-pg., 2019-08-01.

Resumo

In this paper we analyze the asymptotic behavior of a family of solutions of a semilinear elliptic equation, with homogeneous Neumann boundary condition, posed in a two-dimensional oscillating region with reaction terms concentrated in a neighborhood of the oscillatory boundary theta(epsilon) subset of Omega(epsilon) subset of R-2 when a small parameter epsilon > 0 goes to zero. Our main result is concerned with the upper and lower semicontinuity of the set of solutions in H-1. We show that the solutions of our perturbed equation can be approximated with one defined in a fixed limit domain, which also captures the effects of reaction terms that take place in the original problem as a flux condition on the boundary of the limit domain. (AU)

• Processo FAPESP: 17/02630-2 - Análise assintótica de equações diferenciais e integrais
• Beneficiário: Marcone Corrêa Pereira
• Modalidade de apoio: Auxílio à Pesquisa - Regular