01/11 -- 13h00 - 13h50
Stability estimates for recovery of the nonlinearity from scattering data of the Schrodinger equation (Auditório 207 - Pavilhão de Auditórios)
Jayden Julian Bejarano Gonzalez (UFMG)
Models that do not admit Breathers: KdV, Gardner and generalizations (Auditório 207 - Pavilhão de Auditórios)
Victor Ferreira de A. Santos (UFMG)
In this lecture, we will discuss the asymptotic behavior of solutions to the KdV (Korteweg-de Vries) type equation. First, we will identify a class of nonlinear equations of the KdV type for which they do not have Breathers-type solutions. In particular, we will prove that the classical KdV equation does not admit Breathers. Finally we will generalize some results, including the Gardner equation.
01/11 -- 13h50 - 14h40
Unraveling the threshold behavior in Schrödinger equations (Auditório 207 - Pavilhão de Auditórios)
Luccas Campos (UFMG)
In the context of nonlinear, focusing dispersive and wave equations, the associated ground state often gives a quantitative threshold, under which the long-time behavior is well-understood. Such thresholds arise from sharp Gagliardo-Nirenberg-Sobolev inequalities, and initial data below these quantities are subject to the so-called \textit{energy trapping}, which guarantees coercivity for quantities related to the associated potential and kinetic energies. Combined with the concentration-compactness approach, the energy trapping can be used to prove a dichotomy for the asymptotic behavior of H^1 solutions. In this talk, we discuss recent results for Schrödinger-type problems with initial data \textit{exactly} at the mass-energy threshold in the L^2-supercritical setting.
01/11 --14h40 - 15h30
Fundamental frequencies connections with shapes and the isoanisotropic problem (Auditório 207 - Pavilhão de Auditórios)
Raul Fernandes Horta (UFMG)