“The Schrödinger equation in dimension two with a pointwise nonlinearity: a puzzling model”
Thursday, November 28, 2019, 11:00 - Room 2BC30 - Riccardo Adami (Politecnico di Torino)
In opposition to its analogues in dimension one and three, the Schrödinger equation in dimension two with a concentrated nonlinearity displays a behaviour that is, to our knowledge, unprecedented in similar models and not trivial to interpret. After illustrating some physical motivation of the model, we discuss the features of the dynamics it generates, with some emphasis on the blow phenomenon and on stability of standing waves.
This is a joint work with R. Carlone (Napoli), M. Correggi (SNS-Pisa), and L. Tentarelli (Napoli).