On Wednesday June 9, our Head Enrique Zuazua will talk about “Networks, Waves and Control”, an Analysis Seminar of the Department “R. Caccioppoli” at Università degli studi di Napoli Federico II (Italy).
Speaker: Prof. Dr. Enrique Zuazua
Affiliation: FAU Erlangen – Nürnberg (Germany)
Wed. June 9, 2021 at 16:00H (GMT + 2)
Zoom meeting link
Meeting ID: 985 6723 4045 | PIN code: 156654
Abstract. In this lecture we will mainly analyze wave propagation on a planar network. The problem of the observation of waves is a natural framework to address this issue. Roughly, the question can be formulated as follows: Can we recover complete information on the energy of waves by making measurements in one single extreme of the network? This formulation is relevant both in the context of control and inverse problems.
Using the Fourier development of solutions and techniques of Nonharmonic Fourier Analysis, we shall give spectral sharp conditions guaranteeing this property to hold. The analysis becomes much more explicit in the case where the network has a tree-like structure. As a corollary these results can be transferred to other models, such as the Schrödinger, heat or beam-type equations. We shall also present recent results on the uniformity of these results in the context of vanishing viscosity.
Other challenging problems arise in this field. Some of them will be mentioned as topics for future research.