Convidamos todos a participar do CRANED (Colóquio Rio de Janeiro de Análise e Equações Diferenciais), seminário conjunto com UFF, UFRJ, FGV, UERJ, PUC-RIO e IMPA, que será realizado no dia 03/07 (sexta-feira), a partir das 14h, no auditório da Pós-Graduação em Matemática, sala 407 – bloco H – Campus Gragoatá.
Seguem abaixo as informações:
Palestrante 1: Xavier Carvajal
Título e resumo abaixo.
Palestrante 2: Alexei Mailybaev
Title: Hidden Symmetries of Differential Equations: Ideal Fluids and Turbulence
Abstract:
I will discuss hidden symmetries of differential equations that arise from quotient constructions associated with their symmetry groups. These symmetries reveal structures that are not apparent in the original equations and can provide new insights into their dynamics. Particular attention will be given to the Euler equations of ideal fluid dynamics. I will also discuss the role of hidden symmetries in turbulence, including their connection to scale invariance and statistical properties of turbulent flows.
Palestrante 3: Jose Pedro Rodríguez Ayllon-UFF
Title: On Pareto equilibrium for Kirchhoff-type heat equation
Abstract:
This work studies a multiobjective optimal control problem for a generalized heat equation with local nonlinearity. A single agent aims to simultaneously achieve two possibly conflicting objectives, analyzed through the concept of Pareto optimality. Using scalarization techniques, the problem is reduced to a weighted single-objective formulation. For both quasi-linear and bilinear systems, the existence of weak solutions and Pareto optimal controls is established under suitable assumptions. Additionally, conditions ensuring convexity and uniqueness of the optimal control are provided, showing the equivalence between Pareto equilibrium and quasi-equilibrium in relevant cases.
Esperamos vocês!
