Banca de DEFESA: JANDEILSON SANTOS DA SILVA
Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.DISCENTE: JANDEILSON SANTOS DA SILVA
DATA : 11/07/2025
HORA: 14:00
LOCAL: Sala 209
TÍTULO:
Titulo: Control results for the Korteweg-de Vries type equations
PALAVRAS-CHAVES:
Dispersive equations; Boundary controllability; Critical lengths; Return method; Star-graphs; Flatness approach.
PÁGINAS: 185
RESUMO:
This thesis investigates boundary controllability for dispersive systems governed by the Korteweg-de Vries (KdV) type equation. The main goal is to steer the system’s state using boundary controls. We first focus on the well-known KdV equation in a bounded domain with purely Neumann boundary conditions and a single control input. A central difficulty arises when the spatial domain length is critical, rendering the associated linear system uncontrollable. To address this, we employ the return method to establish controllability of the nonlinear system. The second problem considers the KdV equation on a starshaped graph, modeled as a system of N KdV-type equations defined on intervals $(0, \ell_j)$, coupled through a condition at the central node. We demonstrate controllability using $N$ boundary controls, which may be Neumann, Dirichlet, or a combination of both. We identify the corresponding sets of critical lengths through detailed spectral analysis for each boundary configuration. Lastly, we explore the controllability of the fifth-order KdV equation, also namely the Kawahara equation, using two boundary controls. Here, we adopt the flatness method—a nonstandard approach that bypasses the need for an observability inequality. This method expresses the state and control variables in terms of so-called “flat outputs” in Gevrey spaces. Within this framework, we address two key problems: achieving null controllability and characterizing the set of states reachable from zero, thereby identifying a functional space where exact controllability holds.
MEMBROS DA BANCA:
Externo à Instituição - HUGO PARADA RIOS
Externo à Instituição - CHULKWANG KWAK
Interno - 3090383 - CILON VALDEZ FERREIRA PERUSATO
Externo à Instituição - FERNANDO ANDRÉS GALLEGO RESTREPO - UNC
Presidente - 2257161 - ROBERTO DE ALMEIDA CAPISTRANO FILHO