On exact controllability of networks of nonlinear elastic strings in 3-dimensional space
Leugering G, Schmidt GE (2012)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2012
Journal
Book Volume: 33
Pages Range: 33-60
Journal Issue: 1
DOI: 10.1007/s11401-011-0693-9
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. © 2012 Fudan University and Springer-Verlag Berlin Heidelberg.
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APA:
Leugering, G., & Schmidt, G.E. (2012). On exact controllability of networks of nonlinear elastic strings in 3-dimensional space. Chinese Annals of Mathematics Series B, 33(1), 33-60. https://dx.doi.org/10.1007/s11401-011-0693-9
MLA:
Leugering, Günter, and Georg E.P.J. Schmidt. "On exact controllability of networks of nonlinear elastic strings in 3-dimensional space." Chinese Annals of Mathematics Series B 33.1 (2012): 33-60.
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