On Exact Controllability of Networks of Nonlinear Elastic Strings in 3-Dimensional Space |
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Authors: | Günter R Leugering E J P Georg Schmidt |
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Institution: | (1) Department of Mathematics, Friedrich-Alexander University, Erlangen-Nuremberg, Martensstrasse 3, D 91085 Erlangen, Germany;(2) Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, H3A 2K6, Canada |
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Abstract: | This paper concerns a system of nonlinear wave equations describing the vibrations of a 3-dimensional network of elastic strings.
The authors derive the equations and appropriate nodal conditions, determine equilibrium solutions, and, by using the methods
of quasilinear hyperbolic systems, prove that for tree networks the natural initial, boundary value problem has classical
solutions existing in neighborhoods of the “stretched” equilibrium solutions. Then the local controllability of such networks
near such equilibrium configurations in a certain specified time interval is proved. Finally, it is proved that, given two
different equilibrium states satisfying certain conditions, it is possible to control the network from states in a small enough
neighborhood of one equilibrium to any state in a suitable neighborhood of the second equilibrium over a sufficiently large
time interval. |
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Keywords: | Nonlinear strings Network Quasilinear system of hyperbolic equations Controllability |
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