Seminario del prof. Corrado Mascia (Dipartimento di Matematica "G. Castelnuovo", Sapienza Università di Roma).
The talk concerns with the large-time behavior of a class of hyperbolic systems of partial differential equations and its relation with corresponding (reduced) parabolic equations. The basic prototype is the Goldstein-Kac model for correlated random walks, interpreted as a variation of the classical heat equation. Areas of interest of the topic will be presented, together with a selection of known rigorous mathematical results available in the literature. Additionally, the asymptotic description of a generalization of the Goldstein-Kac model to an arbitrary number of speeds in several dimensions (based on an application of a variant of the Kirchoff’s matrix tree Theorem from graph theory) will be presented in details.