Boris Pavlov: Resonance dynamics and local perturbation analysis

Lord Rayleigh published in 1916 a paper where he discussed spectral properties and dynamics the of Helmholtz resonator. Fifty years laterPeter Lax and Ralph Phillips succeeded to insert a solid mathematical basement under the paper of 1916. We will discuss a special local inverse problem, which allows to reveal essential features of the resonance dynamics based on local perturbation analysis. Though the question on bridging both issues has a general meaning, we consider now only a fitted local solvable model for a star-graph network which is reduced to the classical Friedrichs model on Lax-Phillips background.