Banca de QUALIFICAÇÃO: LÁZARO SANTOS GIL

Uma banca de QUALIFICAÇÃO de DOUTORADO foi cadastrada pelo programa.
DISCENTE: LÁZARO SANTOS GIL
DATA: 26/08/2024
HORA: 14:00
LOCAL: sala virtual - defesa remota
TÍTULO: On Inhomogeneous Nonlinear Schödinger Systems Coupled: Well-posedness and Asymptotic Behavior
PALAVRAS-CHAVES: Well posedness; nonlinear Schrödinger equation; stability; blow-up
PÁGINAS: 22
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Matemática
RESUMO:

The behavior of solutions (i.e., scattering and blow up in finite time) for a system of nonlinear Schroedinger (NLS) equations with a general quadratic-type nonlinearity was established by Nogueira and Pastor. In this talk we discuss how to extend their results to the Inhomogeneous coupled NLS system. Under certain assumptions on the coupled terms we prove conservation laws, the existence of solutions and their long-term behavior. More precisely, we show the well-posedness in the subcritical case, conditions for the global existence of solutions, existence of the ground states, sufficient conditions for the global existence and the dichotomy between the finite time blow-up and the existence of a global solution in the intercritical case.

MEMBROS DA BANCA:
Interno - 2240233 - GLEISON DO NASCIMENTO SANTOS
Externo à Instituição - LUIZ GUSTAVO FARAH DIAS - UFMG
Presidente - 2060014 - MYKAEL DE ARAUJO CARDOSO