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Semilinear elliptic equations in thin regions with terms concentrating on oscillatory boundaries

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Arrieta Algarra, José María and Nogueira, Ariadne and Pereira, Marcone C. (2019) Semilinear elliptic equations in thin regions with terms concentrating on oscillatory boundaries. Computers & Mathematics with Applications, 77 (2). pp. 536-554. ISSN 08981221

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Official URL: https://doi.org/10.1016/j.camwa.2018.09.056




Abstract

In this work we study the behavior of a family of solutions of a semilinear elliptic equation, with homogeneous Neumann boundary condition, posed in a two-dimensional oscillating thin region with reaction terms concentrated in a neighborhood of the oscillatory boundary. Our main result is concerned with the upper and lower semicontinuity of the set of solutions. We show that the solutions of our perturbed equation can be approximated with one of a one-dimensional equation, which also captures the effects of all relevant physical processes that take place in the original problem.


Item Type:Article
Uncontrolled Keywords:Semilinear elliptic equations, Singular elliptic equations, Upper semicontinuity, Lower semicontinuity, Thin domains, Concentrating terms
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:54908
Deposited On:04 Apr 2019 18:11
Last Modified:05 Apr 2019 07:16

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