Abstract:
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.
(The talk is based on some old and new joint papers with Marina Ghisi)
Il seminario avrà luogo in presenza presso il Dipartimento di Matematica e Fisica, L.go S. L. Murialdo 1 - Aula 311
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