Seminari del Dipartimento
Analisi Matematica Kirchhoff equation from PDEs to dynamical systems: old challenges and recent advances Massimo Gobbino 30-11-2022 - 16:30 Largo San Leonardo Murialdo, 1 - Aula 311
Kirchhoff hyperbolic equation has attracted a considerable attention since it was introduced in 1976. Nevertheless, many basic questions are still open, in particular whether global solutions exist for all initial data in Sobolev spaces. In this talk we review the main classical results concerning local and global existence, and the difficulties that arise when dealing with the main open problem. We also discuss the stability of simple modes, namely periodic trajectories with only one Fourier component in the space variables, and we show how the existence of a heteroclinic connection between two such trajectories would lead to a solution that blows up in finite time. |