Based on the homotopy analysis method, a general analytic technique for strongly nonlinear problems, a Maple package of automated derivation （ADHO） for periodic nonlinear oscillation systems is presented. This Maple...Based on the homotopy analysis method, a general analytic technique for strongly nonlinear problems, a Maple package of automated derivation （ADHO） for periodic nonlinear oscillation systems is presented. This Maple package is valid for periodic oscillation systems in rather general, and can automatically deliver the accurate approximations of the frequency co and the mean of motion δof a nonlinear periodic oscillator. Based on the homotopy analysis method which is valid even for highly nonlinear problems, this Maple package can give accurate approximate expressions even for nonlinear oscillation systems with strong nonlinearity. Besides, the package is user-friendly： One just needs to input a governing equation and initial conditions, and then gets satisfied analytic approximations in few seconds. Several different types of examples are given in this paper to illustrate the validity of this Maple package. Such kind of package provides us a helpful and easy-to-use tool in science and engineering to analyze periodic of this Maple package from the is published publicly. nonlinear oscillations. And it is free address http：//numericaltank.sjtu to download the electronic version edu.cn/sjliao.htm once the paper展开更多
The authors establish several estimates showing that the distance in W^(1,p),1 < p < ∞,between two immersions from a domain of R^n into R^(n+1) is bounded by the distance in L^p between two matrix fields define...The authors establish several estimates showing that the distance in W^(1,p),1 < p < ∞,between two immersions from a domain of R^n into R^(n+1) is bounded by the distance in L^p between two matrix fields defined in terms of the first two fundamental forms associated with each immersion. These estimates generalize previous estimates obtained by the authors and P. G. Ciarlet and weaken the assumptions on the fundamental forms at the expense of replacing them by two different matrix fields.展开更多
In this paper, the authors consider the Gevrey class regularity of a semigroup associated with a nonlinear Korteweg-de Vries （KdV for short） equation. By estimating the resolvent of the corresponding linear operator...In this paper, the authors consider the Gevrey class regularity of a semigroup associated with a nonlinear Korteweg-de Vries （KdV for short） equation. By estimating the resolvent of the corresponding linear operator, the authors conclude that the semigroup 3 generated by the linear operator is not analytic but of Gevrey class δ ε （5, ） for t 〉 0,展开更多
This paper investigates the nonlinear dynamics of network-based dynamical systems where network communication channels of finite data rates are inserted into the closed loops of the control systems. The authors analyz...This paper investigates the nonlinear dynamics of network-based dynamical systems where network communication channels of finite data rates are inserted into the closed loops of the control systems. The authors analyze the bifurcation and chaotic behavior of the non-smooth dynamical systems. The authors first prove that for almost all system parameters there are no periodic orbits. This result distinguishes this type of non-smooth dynamical systems from many others exhibiting border-collision bifurcations. Next, the authors show analytically that the chaotic sets are separated from the region containing the line segment of all fixed points with a finite distance. Finally, the authors employ a simple model to highlight that both the number of clients sharing a common network channel and fluctuations in the available network bandwidth have significant influence on the performance of such dynamical systems.展开更多
The authors investigate the influence of a harmonic potential and random perturbations on the nonlinear Schr6dinger equations. The local and global well-posedness are proved with values in the space ∑（R^n）={f E HI...The authors investigate the influence of a harmonic potential and random perturbations on the nonlinear Schr6dinger equations. The local and global well-posedness are proved with values in the space ∑（R^n）={f E HI（R^n）, ｜·｜f ∈ L^2（R^n）}. When the nonlinearity is focusing and L2-supercritical, the authors give sufficient conditions for the solutions to blow up in finite time for both confining and repulsive potential. Especially for the repulsive case, the solution to the deterministic equation with the initial data satisfying the stochastic blow-up condition will also blow up in finite time. Thus, compared with the deterministic equation for the repulsive case, the blow-up condition is stronger on average, and depends on the regularity of the noise. If φ = 0, our results coincide with the ones for the deterministic equation.展开更多
基金supported by the National Science Foundation of China under Grant No.11071274
文摘Based on the homotopy analysis method, a general analytic technique for strongly nonlinear problems, a Maple package of automated derivation （ADHO） for periodic nonlinear oscillation systems is presented. This Maple package is valid for periodic oscillation systems in rather general, and can automatically deliver the accurate approximations of the frequency co and the mean of motion δof a nonlinear periodic oscillator. Based on the homotopy analysis method which is valid even for highly nonlinear problems, this Maple package can give accurate approximate expressions even for nonlinear oscillation systems with strong nonlinearity. Besides, the package is user-friendly： One just needs to input a governing equation and initial conditions, and then gets satisfied analytic approximations in few seconds. Several different types of examples are given in this paper to illustrate the validity of this Maple package. Such kind of package provides us a helpful and easy-to-use tool in science and engineering to analyze periodic of this Maple package from the is published publicly. nonlinear oscillations. And it is free address http：//numericaltank.sjtu to download the electronic version edu.cn/sjliao.htm once the paper
基金supported by the Research Grants Council of the Hong Kong Special Administration Region,China(No.9042388,CityU 11305716)
文摘The authors establish several estimates showing that the distance in W^(1,p),1 < p < ∞,between two immersions from a domain of R^n into R^(n+1) is bounded by the distance in L^p between two matrix fields defined in terms of the first two fundamental forms associated with each immersion. These estimates generalize previous estimates obtained by the authors and P. G. Ciarlet and weaken the assumptions on the fundamental forms at the expense of replacing them by two different matrix fields.
基金supported by the National Natural Science Foundation of China(Nos.11401021,11471044,11771336,11571257)the LIASFMA,the ANR project Finite4SoS(No.ANR 15-CE23-0007)the Doctoral Program of Higher Education of China(Nos.20130006120011,20130072120008)
文摘In this paper, the authors consider the Gevrey class regularity of a semigroup associated with a nonlinear Korteweg-de Vries （KdV for short） equation. By estimating the resolvent of the corresponding linear operator, the authors conclude that the semigroup 3 generated by the linear operator is not analytic but of Gevrey class δ ε （5, ） for t 〉 0,
基金supported by an the National Natural Science Foundation of China under Grant No.60804015,and an NSERC grant to the third author
文摘This paper investigates the nonlinear dynamics of network-based dynamical systems where network communication channels of finite data rates are inserted into the closed loops of the control systems. The authors analyze the bifurcation and chaotic behavior of the non-smooth dynamical systems. The authors first prove that for almost all system parameters there are no periodic orbits. This result distinguishes this type of non-smooth dynamical systems from many others exhibiting border-collision bifurcations. Next, the authors show analytically that the chaotic sets are separated from the region containing the line segment of all fixed points with a finite distance. Finally, the authors employ a simple model to highlight that both the number of clients sharing a common network channel and fluctuations in the available network bandwidth have significant influence on the performance of such dynamical systems.
基金supported by the National Natural Science Foundation of China (Nos. 10871175,10931007,10901137)the Zhejiang Provincial Natural Science Foundation of China (No. Z6100217)the Specialized ResearchFund for the Doctoral Program of Higher Education (No. 20090101120005)
文摘The authors investigate the influence of a harmonic potential and random perturbations on the nonlinear Schr6dinger equations. The local and global well-posedness are proved with values in the space ∑（R^n）={f E HI（R^n）, ｜·｜f ∈ L^2（R^n）}. When the nonlinearity is focusing and L2-supercritical, the authors give sufficient conditions for the solutions to blow up in finite time for both confining and repulsive potential. Especially for the repulsive case, the solution to the deterministic equation with the initial data satisfying the stochastic blow-up condition will also blow up in finite time. Thus, compared with the deterministic equation for the repulsive case, the blow-up condition is stronger on average, and depends on the regularity of the noise. If φ = 0, our results coincide with the ones for the deterministic equation.
