Banca de DEFESA: ANDRE LUIZ MENDES XAVIER

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
DISCENTE: ANDRE LUIZ MENDES XAVIER
DATA : 17/07/2025
HORA: 14:00
LOCAL: Sala 209
TÍTULO:

Exponential decay for the Korteweg-de Vries equation on the real line with new classes of localized damping

PALAVRAS-CHAVES:

Korteweg-de Vries; KdV equation; exponential decay; localized damping; Bourgain spaces

 

PÁGINAS: 112
RESUMO:

This master's thesis investigates the results of exponential decay in the \(L^2\) norm of the Korteweg-de Vries (KdV) equation on the real line with localized damping, as established by M.~Wang and D.~Xhou in \cite{Wang1}. Initially, it is proven that for the linear KdV equation, the exponential decay occurs if and only if the average of the damping coefficient across all intervals of a fixed length has a positive lower bound. Subsequently, Bourgain spaces \( X^{s,b} \) are introduced to demonstrate that, under the same damping conditions, exponential decay is also valid for the (nonlinear) KdV equation with small initial data. Finally, with the help of certain properties of regularity propagation in Bourgain spaces for solutions of the associated linear system and the unique continuation property, it is established that the exponential decay for the KdV equation with large initial data holds if the damping coefficient has a positive lower bound in \(E\subset\mathbb{R}\), where \(E\) is equidistributed over the real line and the complement \(E^{c}\) has finite Lebesgue measure. 

 

 

MEMBROS DA BANCA:
Externo à Instituição - ANDRÉ VICENTE - UNIOESTE
Interno - 2257161 - ROBERTO DE ALMEIDA CAPISTRANO FILHO
Presidente - 3310115 - VICTOR HUGO GONZALEZ MARTINEZ