A time-dependent metric graph with a fourth-order operator on the edges

I. V. Blinova, A. S. Gnedash, I. Y. Popov

Department of Higher Mathematics, ITMO University, St. Petersburg, Russia

Abstract: The metric graph model is suggested for description of elastic vibration in a network of rods under the assumption that the rod lengths vary in time. A single rod and star-like graph are considered. Influence of the length variation law on the vibration distribution is investigated. For high-frequency length variation one observes a fast transition to high-frequency amplitude distribution.

Keywords: metric graph, spectrum, time evolution.

MSC: Primary 74K10; Secondary 35G16

Received: 28.09.2020
Accepted: 12.06.2021

Language: English

DOI: 10.2298/TAM200928007B

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