Einladung zum Vortrag (Zoom) von Herrn Prof. Dr. Enzo Vitillaro am 10.02.2021 - 17:00 Uhr im Rahmen des Forschungsseminars Analysis[10.02.2021]
Im Rahmen des Forschungsseminars Analysis hält am Mittwoch, den 10. Februar 2021, um 17:00 Uhr,
Herr Prof. Dr. Enzo Vitillaro (University of Perugia, Italy)
einen Vortrag zum Thema
The wave equation with acoustic boundary conditions
Abstract: The aim of the talk is to give some recent results, obtained in a collaboration (still in progress) with Delio Mugnolo, on the wave equation with acoustic boundary conditions, which has been subject of a large literature starting from the original analysis of Beale and Rosencrans in the 70’s and continuing up today, where the effect of nonlinear perturbations of any type is studied. In particular, after summarizing well-posedness and regularity results in the associated energy space, we shall show that for a bounded domain some physically inexplicable stationary solutions make the problem not asymptotically stable, even with an effective damping, while it is asymptotically stable provided that the initial data are restricted to a 1-codimensional subspace, which is invariant under the flow.
This mathematical result leads to a physical re-thinking of the derivation of the model itself in Theoretical Acoustic. In particular, starting from Newton’s Second Law, we shall show that the PDEs appearing in it need to be integrated with an integral condition which is exactly the one found in the stability analysis of it, a fact never observed in the existing literature.
Der Vortrag findet im Rahmen eines Zoom-Meetings statt. Bei Interesse an den Zugangsdaten bitte bei Herrn Prof. Dr. Mugnolo (firstname.lastname@example.org) melden.