Banca de DEFESA: LÁZARO SANTOS GIL

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
DISCENTE: LÁZARO SANTOS GIL
DATA: 30/07/2026
HORA: 15:00
LOCAL: Programa de Pós-graduação em Matemática
TÍTULO: On Inhomogeneous Nonlinear Schödinger Systems Coupled: Well-posedness and Asymptotic Behavior
PALAVRAS-CHAVES: Well posedness; nonlinear Schrödinger equation; stability; blow-up
PÁGINAS: 144
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Matemática
SUBÁREA: Análise
ESPECIALIDADE: Equações Diferenciais Parciais
RESUMO:

The behavior of solutions, namely scattering and finite-time blow-up, for systems of nonlinear Schrödinger (NLS) equations with general quadratic-type nonlinearities was established by Nogueira and Pastor. In this thesis, we extend these results to a coupled inhomogeneous NLS system. Under suitable assumptions on the nonlinear coupling terms, we establish conservation laws, local and global well-posedness, and the long-time behavior of solutions. More precisely, we prove well-posedness in the mass-subcritical regime, establish the existence of ground states, derive sufficient conditions for global existence, and characterize the dichotomy between global existence and finite-time blow-up in the intercritical regime. Finally, we prove scattering for radial solutions in the intercritical regime. The argument combines Strichartz estimates, Morawetz-type estimates, and a scattering criterion inspired by the works of Guzmán and Campos. The analysis is carried out without assuming a mass-resonance condition, thereby extending the applicability of previous scattering results.

MEMBROS DA BANCA:
Presidente - 2060014 - MYKAEL DE ARAUJO CARDOSO
Interno - 1391774 - AILTON CAMPOS DO NASCIMENTO
Interno - 2240233 - GLEISON DO NASCIMENTO SANTOS
Interno - 1858579 - JOSE FRANCISCO ALVES DE OLIVEIRA
Externo à Instituição - 038.***.***-60 - LUIZ GUSTAVO FARAH DIAS - UFMG
Externo à Instituição - 076.***.***-23 - MARCIO CAVALCANTE DE MELO - UFAL