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
In this paper, we discuss the blow-up of periodic solutions to a class of quasilinear hyperbolic systems in diagonal form, and make the accurate estimate of life-span. These results in this paper extend the conclusion...In this paper, we discuss the blow-up of periodic solutions to a class of quasilinear hyperbolic systems in diagonal form, and make the accurate estimate of life-span. These results in this paper extend the conclusion [1-3].展开更多
In this paper the authors consider Cauchy problem of first order quasilinear hyperbolic and prove that existence of its periodic solutions and estimates of life span of solutions. This results reveals the relationship...In this paper the authors consider Cauchy problem of first order quasilinear hyperbolic and prove that existence of its periodic solutions and estimates of life span of solutions. This results reveals the relationship of dissipation and smoothness of periodic solutions.展开更多
该文以交通流模型中不同平衡函数表达式为例,对一阶非线性双曲型方程组的自由项形式与数值解的色散性、耗散性之间关系,进行了数值模拟研究。结果发现:自由项对方程组数值解的色散性和耗散性影响都是比较有规律的,这种规律性在不同初始...该文以交通流模型中不同平衡函数表达式为例,对一阶非线性双曲型方程组的自由项形式与数值解的色散性、耗散性之间关系,进行了数值模拟研究。结果发现:自由项对方程组数值解的色散性和耗散性影响都是比较有规律的,这种规律性在不同初始密度条件下是不一样的;自由项导致方程组数值解色散或耗散强弱,与方程组的离散方式也有关,尤其在中等密度条件下。就Payne-W h itham模型方程,建议了能够对不同初始密度下扰动的传播和发展进行合理数值模拟的自由项和离散方式。展开更多
For first-order quasilinear hyperbolic systems with zero eigenvaiues, the author establishes the local exact controllability in a shorter time-period by means of internal controls acting on suitable domains. In partic...For first-order quasilinear hyperbolic systems with zero eigenvaiues, the author establishes the local exact controllability in a shorter time-period by means of internal controls acting on suitable domains. In particular, under certain special but reasonable hypotheses, the local exact controllability can be realized only by internal controls, and the control time can be arbitrarily small.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In this paper, we discuss the blow-up of periodic solutions to a class of quasilinear hyperbolic systems in diagonal form, and make the accurate estimate of life-span. These results in this paper extend the conclusion [1-3].
文摘In this paper the authors consider Cauchy problem of first order quasilinear hyperbolic and prove that existence of its periodic solutions and estimates of life span of solutions. This results reveals the relationship of dissipation and smoothness of periodic solutions.
文摘该文以交通流模型中不同平衡函数表达式为例,对一阶非线性双曲型方程组的自由项形式与数值解的色散性、耗散性之间关系,进行了数值模拟研究。结果发现:自由项对方程组数值解的色散性和耗散性影响都是比较有规律的,这种规律性在不同初始密度条件下是不一样的;自由项导致方程组数值解色散或耗散强弱,与方程组的离散方式也有关,尤其在中等密度条件下。就Payne-W h itham模型方程,建议了能够对不同初始密度下扰动的传播和发展进行合理数值模拟的自由项和离散方式。
文摘For first-order quasilinear hyperbolic systems with zero eigenvaiues, the author establishes the local exact controllability in a shorter time-period by means of internal controls acting on suitable domains. In particular, under certain special but reasonable hypotheses, the local exact controllability can be realized only by internal controls, and the control time can be arbitrarily small.
