Control and inverse problems for networks of vibrating strings with attached masses
https://doi.org/10.17586/2220-8054-2016-7-5-835-841
Abstract
We consider the control and inverse problems for serially connected and tree-like networks of strings with point masses loaded at the internal vertices. We prove boundary controllability of the systems and the identifiability of varying coefficients of the string equations along with the complete information on the graph, i.e. the loaded masses, the lengths of the edges and the topology (connectivity) of the graph. The results are achieved using the Titchmarch-Weyl function for the spectral problem and the Steklov-Poincare operator for the dynamic wave equation on the tree. The general result is obtained by the leaf peeling method which reduces the inverse problem layer-by-layer from the leaves to the fixed root of the tree.
Supporting agencies: The research of S.Avdonin was supported in part by the National Science Foundation, grant DMS1411564 and by the Ministry of Education and Science of Republic of Kazakhstan under the grant No. 4290/GF4.
About the Authors
F. Al-Musallam
Department of Mathematics, Kuwait University
Kuwait
Kuwait
P.O Box 5969 Safat
S. Avdonin
Department of Mathematics and Statistics, University of Alaska
United States
United States
Fairbanks, AK 99775
N. Avdonina
Department of Mathematics and Statistics, University of Alaska
United States
United States
Fairbanks, AK 99775
J. Edward
Department of Mathematics and Statistics, Florida International University
United States
United States
Miami, FL 33199
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Review
For citations:
Al-Musallam F., Avdonin S., Avdonina N., Edward J. Control and inverse problems for networks of vibrating strings with attached masses. Nanosystems: Physics, Chemistry, Mathematics. 2016;7(5):835-841. https://doi.org/10.17586/2220-8054-2016-7-5-835-841
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