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| Exact Boundary Controllability on a Tree-Like Network of NonlinearPlanar Timoshenko Beams |
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Citation： |
Qilong GU,Gunter LEUGERING,Tatsien LI.Exact Boundary Controllability on a Tree-Like Network of NonlinearPlanar Timoshenko Beams[J].Chinese Annals of Mathematics B,2017,38(3):711~740 |
| Page view： 4491
Net amount： 3712 |
Authors： |
Qilong GU; Gunter LEUGERING;Tatsien LI |
Foundation： |
This work was supported by the National Basic Research
Program of China (No.2103CB834100), the National Science
Foundation of China (No.11121101), the National Natural Sciences
Foundation of China (No.11101273) and the DFG-Cluster of
Excellence: Engineering of Advanced Materials. |
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| Abstract： |
This paper concerns a system of equations describing the vibrations
of a planar network of nonlinear Timoshenko beams. The authors
derive the equations and appropriate nodal conditions, determine
equilibrium solutions and, using the methods of quasilinear
hyperbolic systems, prove that for tree-like networks the natural
initial-boundary value problem admits semi-global classical
solutions in the sense of Li [Li, T. T., Controllability and
Observability for Quasilinear Hyperbolic Systems, AIMS Ser. Appl.
Math., vol 3, American Institute of Mathematical Sciences and Higher
Education Press, 2010]existing in a neighborhood of the equilibrium
solution. The authors then prove the local exact controllability of
such networks near such equilibrium configurations in a certain
specified time interval depending on the speed of propagation in the
individual beams. |
Keywords： |
Nonlinear Timoshenko beams, Tree-like networks, Exact boundary
controllability, Semi-global classical solutions |
Classification： |
35L70, 93B05, 49J40 |
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