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...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.展开更多
The author establishes the exact boundary observability of unsteady supercritical flows in a tree-like network of open canals with general topology. An implicit duality between the exact boundary controllability and t...The author establishes the exact boundary observability of unsteady supercritical flows in a tree-like network of open canals with general topology. An implicit duality between the exact boundary controllability and the exact boundary observability is also given for unsteady supercritical flows.展开更多
基金supported by the National Basic Research Program of China(No.2103CB834100)the National Science Foundation of China(No.11121101)+1 种基金the National Natural Sciences Foundation of China(No.11101273)the DFG-Cluster of Excellence:Engineering of Advanced Materials
文摘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.
文摘The author establishes the exact boundary observability of unsteady supercritical flows in a tree-like network of open canals with general topology. An implicit duality between the exact boundary controllability and the exact boundary observability is also given for unsteady supercritical flows.
