Controlabilidade exata de sistemas parabólicos, hiperbólicos e dispersivos

• Autor(a) principal: Santos, Maurício Cardoso
• Data de Publicação: 2014
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFPB
• Texto Completo: https://repositorio.ufpb.br/jspui/handle/tede/7432
• topic: Controlabilidade; Estratégias do tipo Stackelberg-Nash; Desigualdade de Carleman; Equação de Schrödinger-1D; Equação do Calor; Equação KdV; Elementos finitos; Sistema de Boussinesq-Invíscido; Controllability; Stackelberg-Nash strategies; Carleman inequalities; 1D Schrödinger equation; Heat Equation; KdV equation; Finite element methods; Carleman inequalities; Inviscid Boussinesq system; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this thesis, we study controllability results of some phenomena modeled by Partial Differential Equations (PDEs): Multi objective control problem, for parabolic equations, following the Stackelber-Nash strategy is considered: for each leader control which impose the null controllability for the state variable, we find a Nash equilibrium associated to some costs. The leader control is chosen to be the one of minimal cost. Null controllability for the linear Schrödinger equation: with a convenient space-time discretization, we numerically construct boundary controls which lead the solution of the Schrödinger equation to zero; using some arguments of Fursikov-Imanuvilov (see [Lecture Notes Series, Vol 34, 1996]) we construct controls with exponential decay at final time. Null controllability for a Schrödinger-KdV system: in this work, we combine global Carleman estimates with energy estimates to obtain an observability inequality. The controllability result holds by the Hilbert Uniqueness Method (HUM). Controllability results for a Euler type system, incompressible, inviscid, under the influence of a temperature are obtained: we mainly use the extension and return methods