Título:

On a class of singular elliptic equation arising in MEMS modeling

Autor:

ESTEBAN PEREIRA DA SILVA

Tipo de Trabalho de Conclusão:

TESE

Abreviatura:

SILVA, E. P.

Data da Defesa:

12/12/2014

Resumo:

Motivated by recent works on the study of the equations that model the electrostatic MEMS devices, we study the quasilinear elliptic equation    −(r α |u ′ | β u ′ ) ′ = λr γ f(r) (1−u) 2 , r ∈ (0,1), 0 ≤ u(r) ≤ 1, r ∈ (0,1), u ′ (0) = u(1) = 0. (Pλ ) According to the choice of the parameters α, β and γ, the differential operator which we are dealing with corresponds to the radial form of Laplacian, p-Laplacian and k-Hessian. We study the stable branch of positive solutions as well as the first unstable branch. Our focus is on the critical case associated with the parameter λ, i. e., the case λ = λ ∗ , where λ ∗ is a constant that delimits the existence of solutions for problem (Pλ ). Among other results we prove uniqueness for the solution for case λ = λ ∗ , and −1 < β.

Palavras-chave:

quasilinear elliptic equation, p-laplacian, k-Hessian, MEMS capacitor, extremal solutions, minimal solutions, semi-stable solution, regularity, singular nonlinearities, mountain pass.

Abstract:

Motivated by recent works on the study of the equations that model the electrostatic MEMS devices, we study the quasilinear elliptic equation    −(r α |u ′ | β u ′ ) ′ = λr γ f(r) (1−u) 2 , r ∈ (0,1), 0 ≤ u(r) ≤ 1, r ∈ (0,1), u ′ (0) = u(1) = 0. (Pλ ) According to the choice of the parameters α, β and γ, the differential operator which we are dealing with corresponds to the radial form of Laplacian, p-Laplacian and k-Hessian. We study the stable branch of positive solutions as well as the first unstable branch. Our focus is on the critical case associated with the parameter λ, i. e., the case λ = λ ∗ , where λ ∗ is a constant that delimits the existence of solutions for problem (Pλ ). Among other results we prove uniqueness for the solution for case λ = λ ∗ , and −1 < β.

Keywords:

quasilinear elliptic equation, p-laplacian, k-Hessian, MEMS capacitor, extremal solutions, minimal solutions, semi-stable solution, regularity, singular nonlinearities, mountain pass

Volume:

1

Páginas:

48

Idioma:

INGLES

Biblioteca depositada:

Central e Setorial

Autorização de divulgação:

O trabalho possui divulgação autorizada

Anexo:

Tese Esteban Pereira da Silva.pdf

Área de Concentração:

ANÁLISE

Linha de Pesquisa:

EQUAÇÕES DIFERENCIAIS NÃO-LINEARES

Projeto de Pesquisa:

INSTITUTO NACIONAL DE CIÊNCIA E TECNOLOGIA DE MATEMÁTICA - INCTMAT

Orientador:

JOAO MARCOS BEZERRA DO O

O orientador principal compôs a banca do discente?:

Não

Tipo de Vínculo Empregatício:

Servidor Público

Tipo de Instituição:

Instituição de Ensino e Pesquisa

Expectativa de Atuação:

Ensino e Pesquisa

Mesma Área de Atuação?

Sim