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Chinese Annals of Mathematics, Series B

, Volume 38, Issue 3, pp 711–740 | Cite as

Exact boundary controllability on a tree-like network of nonlinear planar Timoshenko beams

  • Qilong Gu
  • Günter LeugeringEmail author
  • Tatsien Li
Article

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 

2000 MR Subject Classification

35L70 93B05 49J40 

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Copyright information

© Fudan University and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Department MathematikFriedrich-Alexander University Erlangen-NurembergErlangenGermany
  3. 3.School of Mathematical SciencesFudan UniversityShanghaiChina
  4. 4.Shanghai Key Laboratory for Contemporary Applied MathematicsFudan UniversityShanghaiChina
  5. 5.Nonlinear Mathematical Modeling and Methods LaboratoryFudan UniversityShanghaiChina

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