The N involutive integrals of motion with linearly independent gradients for the nonlin earized eigenvalue problem corresponding to the classical Boussinesq (CB) hierarchy are given. It is shown that when n=1,2,3, the...The N involutive integrals of motion with linearly independent gradients for the nonlin earized eigenvalue problem corresponding to the classical Boussinesq (CB) hierarchy are given. It is shown that when n=1,2,3, the nonlinearized time parts of Lax systems for the CB hierarchy are transformed into three finite-dimensional integrable Hamiltonian systems under the constraint of the nonlinearized spatial part.展开更多
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
文摘The N involutive integrals of motion with linearly independent gradients for the nonlin earized eigenvalue problem corresponding to the classical Boussinesq (CB) hierarchy are given. It is shown that when n=1,2,3, the nonlinearized time parts of Lax systems for the CB hierarchy are transformed into three finite-dimensional integrable Hamiltonian systems under the constraint of the nonlinearized spatial part.
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.
