Il prossimo incontro del ciclo dei “Seminari di Analisi junior” si terrà venerdì 17 gennaio 2025 alle ore 15.00, nella Sala Riunioni 1° Livello. Di seguito, riportiamo i nomi dei due speaker e gli abstract dei loro talk.

Ilenia Di Giorgio :  Normalized NLS ground states on a double plane hybrid
Abstract:  In this talk, I will present a novel model of a quantum hybrid, consisting of two planes interconnected at a single point. We explore the existence and characteristics of normalized ground states within a nonlinear Schrödinger equation, specifically focusing on how these states are influenced by key model parameters. Additionally, we will analyze the distribution of mass across the two planes and examine variations in the strengths of the logarithmic singularities on each plane, as influenced by changes in the matching condition parameters and the powers of the nonlinear terms.

Salvatore Niro:  Approximation of nonlinear Dirac dynamics
Abstract: We consider the nonlinear Dirac equations in one dimension and review various results on global existence of solutions in Sobolev space. Then we define and study the Cauchy problem for a nonlinear Dirac equation with nonlinearities concentrated at one point and its approximations by means of scaled regular potentials. We see in which sense the full dynamics is recovered in the short-range limit and we discuss some characteristic features of the relativistic interactions.