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| On Exact Controllability of Networks of Nonlinear Elastic Strings in 3-Dimensional Space |
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Citation： |
Günter R. LEUGERING,E. J. P. Georg SCHMIDT.On Exact Controllability of Networks of Nonlinear Elastic Strings in 3-Dimensional Space[J].Chinese Annals of Mathematics B,2012,33(1):33~60 |
| Page view： 2729
Net amount： 2298 |
Authors： |
Günter R. LEUGERING; E. J. P. Georg SCHMIDT; |
Foundation： |
the DFG SPP1253: Optimization with PDE-Constaints, and the DFG-CE315 Cluster of Excellence: Engineering of Advanced Materials. |
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| Abstract： |
This paper concerns a system of nonlinear wave equations describing the vibrationsof a 3-dimensional network of elastic strings. The authors derive the equations andappropriate nodal conditions, determine equilibrium solutions, and, by using the methodsof quasilinear hyperbolic systems, prove that for tree networks the natural initial, boundaryvalue problem has classical solutions existing in neighborhoods of the “stretched”equilibrium solutions. Then the local controllability of such networks near such equilibriumconfigurations 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 controlthe network from states in a small enough neighborhood of one equilibrium to any state ina suitable neighborhood of the second equilibrium over a sufficiently large time interval. |
Keywords： |
Nonlinear strings, Network, Quasilinear system of hyperbolic equations, Controllability |
Classification： |
35L70,93B05,49J40 |
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