Spectral analysis of a Neumann biharmonic operator on a dumbbell domain
Event details
| Date | 07.12.2016 |
| Hour | 15:00 › 16:15 |
| Speaker | Francesco Ferraresso (Università degli Studi di Padova) |
| Location |
MA 10
|
| Category | Conferences - Seminars |
We discuss the spectral behavior of the biharmonic operator subject to boundary conditions of Neumann type on a planar dumbbell domain, in the spirit of the results obtained by J.M Arrieta and collaborators for the Neumann Laplacian. By dumbbell domain we mean the union of two fixed bounded disjoint domains and a thin channel connecting the two components. The thickness of the channel depends on a small parameter and vanishes as such parameter tends to zero. Thus, in the limit the channel collapses to a segment. We provide a full description of the limiting problem and of its spectrum. In particular, we show that the eigenvalues of the dumbbell problem are of two types: either they converge to an eigenvalue corresponding to the Neumann biharmonic operator in the fixed part of the dumbbell, or they converge to an eigenvalue corresponding to an ordinary differential equation in the segment. Such ODE has a peculiar differential structure, generally different from the original PDE. Finally, we present some results concerning the convergence of the eigenfunctions.
The talk is based on a joint work with J.M. Arrieta and P.D. Lamberti.
The talk is based on a joint work with J.M. Arrieta and P.D. Lamberti.
Practical information
- General public
- Free
Organizer
- Luigi Provenzano