Seminario: Spectral gaps for elastic and piezoelectric waveguides

Giovedì 22 Ottobre 2015, ore 16:30 - Aula 1BC50 - Jari Taskinen



Giovedì 22 Ottobre 2015 alle ore 16:30 in Aula 1BC50, Jari Taskinen (University of Helsinki) terrà un seminario dal titolo "Spectral gaps for elastic and piezoelectric waveguides".

We consider the band-gap structure of linear elasticity and piezoelectricity problems on quasiperiodic 3-dimensional waveguides. We consider waveguides with thin structures, which are created by thin ligaments connecting (infinitely many, translated copies of) bounded cells. We establish the existence of an arbitrary number of gaps, if the connecting ligaments of the cells are thin enough. In the case of the elasticity system we have quite precise information on the position of the spectral bands. The sharpest results are obtained using asymptotic analysis (work with F.Bakharev). In the case of the piezoelectricity system (work with S.Nazarov), the information is less precise, due to high complexity of the problem, and the mere existence of the band-gap structure for the essential spectrum needs a new proof, which we able to provide. Otherwise, the methods include a self-adjoint reduction scheme, max-min-principle and weighted Sobolev estimates.