Apresentador : Profa. Alessia Ascanelli

Filiação: Universidade de Ferrara
Data: 04/06/2025
Horário: 15:00 às 16:00
Local: Anfiteatro, Sala 500 - Depto. de Computação e Matemática

Descrição: This is a joint work with Alexandre Arias Junior (Universidade de São Paulo), Alessia Ascanelli (Università di Ferrara) and Eliakim Machado (Universidade Federal do Paraná). Resumo: In this talk we deal with the Cauchy problem for Schrödinger-type operators with (t, x)−depending non regular coecients; more precisely, the coefficients are assumed to be tempered distributions in the space variable. Due to the remarkable Schwartz impossibility result, the usual concept of solution to this problem makes no sense. We thus need to define a new concept of solution: the Schwartz very weak solution. We are going to prove the existence of a Schwartz very weak solution which is unique modulo negligible perturbations. We also show consistency with the classical theory in the case of regular coefficients and Schwartz Cauchy data. This result comes from a joint work with Alexandre Arias Junior (University of São Paulo, Brasil), Marco Cappiello (University of Torino, Italy) and Claudia Garetto (Queen Mary University of London, UK).