Publicação
Controlabilidade exata de sistemas parabólicos, hiperbólicos e dispersivos
| Resumo: | 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 |
|---|---|
| Autores principais: | Santos, Maurício Cardoso |
| Assunto: | 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 |
| Ano: | 2015 |
| País: | Brasil |
| Tipo de documento: | tese de doutoramento |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | IBICT |
| Idioma: | português |
| Origem: | Oasisbr |
| Resumo: | 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 |
|---|
Atividades financiadas
Não foram encontrados projetos financiados.