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931.
研究一类高维相对转动非线性动力系统的降维与分岔特性. 在考虑转动系统中间隙非线性影响因素的基础上, 基于广义耗散系统拉格朗日原理, 建立了一类高维相对转动非线性系统动力学模型.采用Lyapunov-Schmidt(LS)约化方法, 通过对高维非线性动力系统进行降维处理, 得到能够揭示系统非线性动力特性与系统参数之间规律的低维等价分岔方程. 运用奇异性理论对分岔方程进行普适开折, 分析了系统的分岔特性.结合实例参数, 对分岔特性进行仿真分析, 得到相对转动非线性动力系统发生动力失稳的参数区域及系统参数对动力失稳的影响规律. 相似文献
932.
周期解的分岔广泛存在于实际的非线性动力学系统中.该文对两个状态变量系统的约束分岔进行了讨论.在约束条件下系统将产生新的转迁集.此外,以一个二维系统为例,对含有约束条件和不含有约束条件的分岔特性进行了比较.所得的结果可以为系统的设计和参数选择提供理论依据. 相似文献
933.
A fundamental solution for half-plane problems which will play a key role in calculation of the stress concentration around a hole embedded in half-plane is derived by a method combining images with direct integrations. It is wore intuitive than the Fourier transform method used by Gladwell[6]. In addition, the principle and procedure of boundary element method to solve the half-plane problems are also presented by means of Betti’s reciprocal theorem in this paper.It is shown that the. computing procedure for half-plane problems is much more convenient using the fundamental solution presented here than the one adopted by C.A. 相似文献
934.
徐玉梅 《高校应用数学学报(英文版)》2006,21(4)
This paper deals with the asymptotic behavior of the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with weaker decaying initial data, and obtains a blow-up result for C1 solution to Cauchy problem. 相似文献
935.
Let P be an isolated singularity of multiplicity 4 of a complex surface Y. It is well-known that there is a locally irreducible finite covering π:(Y, P) → (X, p) with π-1(p)=P, and a Jung's resolution f:Ỹ → Y. Let Wp be the exceptional divisor of (π◦f)-1(p). We will prove that Wp has a unique decomposition into fundamental cycles Wp=2Z1 or Wp=Σα=1l Zα satisfying some conditions. We will define a local index wp for π at p and compute it by the above decomposition of Wp. In particular, we will show that (Y, P) is singular iff wp ≥ 1. As another application of the decomposition of Wp, we also compute the number of blown-downs needed to get the minimal resolution from Ỹ. © 2021, Chinese Academy of Sciences. All right reserved. 相似文献
936.
937.
In this note, we prove that the abstract gradient flow introduced by Baird-Fardoun-Regbaoui [2] is well-posed on a closed Riemann surface with conical singularity. Long time existence and convergence of the flow are proved under certain assumptions. As an application, the prescribed Gaussian curvature problem is solved when the singular Euler characteristic of the conical surface is non-positive. 相似文献
938.
It is well known that the damping term will give more smooth effect to obtain global solutions. In this paper, we consider the effect of damping term on the solutions to system of inhomogeneous wave equation with damping term. We can obtain the singularity that will be formed in finite time for some large initial data. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
939.
For m
2 < a
2 + q
2, with m, a, and q respectively the source mass, angular momentum per unit mass, and electric charge, the Kerr–Newman (KN) solution of Einstein's equation reduces to a naked singularity of circular shape, enclosing a disk across which the metric components fail to be smooth. By considering the Hawking and Ellis extended interpretation of the KN spacetime, it is shown that, similarly to the electron-positron system, this solution presents four inequivalent classical states. Making use of Wheeler's idea of charge without charge, the topological structure of the extended KN spatial section is found to be highly non-trivial, leading thus to the existence of gravitational states with half-integral angular momentum. This property is corroborated by the fact that, under a rotation of the space coordinates, those inequivalent states transform into themselves only after a 4 rotation. As a consequence, it becomes possible to naturally represent them in a Lorentz spinor basis. The state vector representing the whole KN solution is then constructed, and its evolution is shown to be governed by the Dirac equation. The KN solution can thus be consistently interpreted as a model for the electron-positron system, in which the concepts of mass, charge and spin become connected with the spacetime geometry. Some phenomenological consequences of the model are explored. 相似文献
940.
Shi-Zhong Du 《Journal of Differential Equations》2019,266(9):5942-5970
Refined structures of blowup for non-collapsing maximal solution to a semilinear parabolic equation with are studied. We will prove that the blowup set is empty for non-collapsing blowing-up in subcritical case, and all finite time non-collapsing blowing-up must be refined type II in critical case. When for , the Hausdorff dimension of the blowup set for maximal solution whose energy is non-collapsing is shown to be no greater than , which answers a question proposed in [7] positively. At the end of this paper, we also present some new examples of collapsing and non-collapsing blowups. 相似文献