Equações Elípticas com não Linearidade Singular que Modelam MEMSs Eletrostáticos

• Autor(a) principal: Silva, Esteban Pereira da
• Data de Publicação: 2010
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFPB
• Texto Completo: https://repositorio.ufpb.br/jspui/handle/tede/7399
• topic: Equações elípticas; MEMS eletrostáticos; Problema de segunda ordem; Problema de quarta ordem; Elliptic equations; Electrostatic MEMS; Problem of second order; Problem of fourth order; CIENCIAS EXATAS E DA TERRA::MATEMATICA

Here we study a class of semilinear elliptic equations with nonlinearity of an inverse square type. This equations arise, in applications, on the modeling of certain electrostatic devices from microtechnology, MEMS - Micro Electro Mechanical Systems. More precisely, these equations characterizes the function that represents the deformation of a deformable capacitor under the influence of an applied voltage. The Mathematical tools used on the study of such problems involve a bit of Nonlinear Analysis and Partial Differential Equations' methods as sub and supersolutions, sign preserving Theorems (Maximum Principle, Boggio's Principle), energy estimates via Sobolev spaces, etc. In a parallel way we wish to emphasize the importance of this investigation, in Mathematics, on helping the understanding on the class of singular problems in Partial Differential Equations.