Exact Boundary Controllability on a Tree-Like Network of NonlinearPlanar Timoshenko Beams

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: 1442        Net amount: 961

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.
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
Download PDF Full-Text

主管单位:国家教育部 主办单位:复旦大学 地址:上海市邯郸路220号复旦大学数学科学学院 E-mail:edcam@fudan.edu.cn

本系统由北京勤云科技发展有限公司提供技术支持