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

查看全文 作　　者：Qilong [1]GU;Günter [2]LEUGERING;Tatsien [3,4]LI

机构地区：[1]School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai 200240,China;[2]Department Mathematik,Friedrich-Alexander University Erlangen-Nuremberg,91058 Erlangen,Germany;[3]School of Mathematical Sciences,Fudan University,Shanghai 200433,China;[4]Shanghai Key Laboratory for Contemporary Applied Mathematics,Nonlinear Mathematical Modeling and Methods Laboratory

出　　处：《Chinese Annals of Mathematics,Series B》索引2017年第38卷第3期,共30页

基　　金：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);the DFG-Cluster of Excellence:Engineering of Advanced Materials 摘　　要：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. 关键词：TIMOSHENKO梁平面非线性树状网络边界能控性拟线性双曲型方程组高等教育出版社精确可控性数学科学

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

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