A NON-OVERLAPPING DOMAIN DECOMPOSITION ALGORITHM BASED ON THE NATURAL BOUNDARY REDUCTION FOR WAVE EQUATIONS IN AN UNBOUNDED DOMAIN

In this paper, a new domain decomposition method based on the natural boundary reduction, which solves wave problems over an unbounded domain, is suggestted. An circular artificial boundary is introduced. The original unbounded domain is divided into two subdomains, an internal bounded region and external unbounded region outside the artificial boundary. A Dirichlet-Neumann(D-N) alternating iteration algorithm is constructed. We prove that the algorithm is equavilent to preconditional Richardson iteration method. Numerical studies are performed by finite element method. The numerical results show that the convergence rate of the discrete D-N iteration is independent of the finite element mesh size.     

Martingale solutions of a stochastic wave equation with reflection

We discuss an initial boundary value problem for a one-dimensional stochastic wave equation with reflection. For stochastic parabolic equations with reflection, there are some well-known results. However, there seems to be no existence result for a stochastic wave equation with reflection. Even for a deterministic wave equation, the problem has not been completely resolved. Our goal is to establish the existence of a martingale solution for this problem.     

Wave motions in a compressible stratified rotating fluid

The dynamics equations for a stratified rotating fluid with a random distribution of stratification are considered. These equations are reduced to a scalar equation using two potential functions. The solvability of the initial-boundary value problems of the wave theory is established.     

波浪中多船近距离并行航行的水动力干扰研究

采用三维势流理论及多体动力学理论建立了波浪中近距离并行航行多船波浪作用力及运动响应的计算模型.为考虑航速效应对船体间自由面的影响,采用三维移动脉动源Green（格林）函数来模拟船间的辐射波及绕射波.采用该数学模型求解了零航速及有航速情形下两船近距离并行时的流体动力项及运动响应,和模型试验结果比较验证了方法的可靠性.将该方法推广至三船并行航行的情形,重点分析了三船并行时水动力干扰和两船并行时水动力干扰的差异.     

Decay estimates for dissipative wave equations in exterior domains

Consider the initial boundary value problem for the linear dissipative wave equation (□+∂_t)u=0 in an exterior domain . Using the so-called cut-off method together with local energy decay and L² decays in the whole space, we study decay estimates of the solutions. In particular, when N?3, we derive L^p decays with p?1 of the solutions. Next, as an application of the decay estimates for the linear equation, we consider the global solvability problem for the semilinear dissipative wave equations (□+∂_t)u=f(u) with f(u)=|u|^α+1,|u|^αu in an exterior domain.     

Injectivity of the Spherical Mean Operator on the Conical Manifolds of Spheres

Let f be a continuous function on ⁿ . If f has zero integral over every sphere intersecting a given subset A of ⁿ and A lies in no affine plane of dimension n -2, then f vanishes identically. The condition on the dimension of A is sharp.     

Blow-up of Solutions of a Quasilinear Wave Equation with Nonlinear Dissipation

In this paper we establish the blow up of solutions to the quasilinear wave equation with a nonlinear dissipative term u_{tt} - M(||A^{1/2}u||²_2)Au + |ut|^βu_t = |u|^pu x ∈ Ω, t > 0     

地基-结构相互作用系统的时域参数识别

提出地基-结构相互作用系统的时域参数识别方法．在建立地基-结构相互作用的计算模式和运动方程的基础上,运用扩展的卡尔曼滤波技术,将相互作用系统中的参数作为增加的状态变量,建立了该系统的时域参数识别方法．并依据大型振动台条件下的层状地基-贮仓结构相互作用系统的模型试验数据,实施了地基-结构相互作用系统时域参数识别的全过程．计算结果表明,该方法产生良好的参数估计．     

Iterated Brownian Motion in Parabola-Shaped Domains

Iterated Brownian motion Z_t serves as a physical model for diffusions in a crack. If τ_D(Z) is the first exit time of this processes from a domain D⊂ℝⁿ, started at z∈D, then P_z[τ_D(Z)>t] is the distribution of the lifetime of the process in D. In this paper we determine the large time asymptotics of which gives exponential integrability of for parabola-shaped domains of the form P_α={(x,Y)∈ℝ×ℝⁿ⁻¹:x>0, |Y|<Ax^α}, for 0<α<1, A>0. We also obtain similar results for twisted domains in ℝ² as defined in DeBlassie and Smits: Brownian motion in twisted domains, Preprint, 2004. In particular, for a planar iterated Brownian motion in a parabola we find that for z∈℘

外部区域上的一类半线性伪抛物型方程

本文主要考虑在外区域上的一类半线性伪抛物型方程的解的长时间行为.本文得到的临界指标揭示了边界上的非齐次条件将对解的长时间行为产生本质影响.     

A priori estimates for a singular limit approximation of the constitutive laws for chiral media in the time domain

The equations for the evolution of electromagnetic fields in chiral media, in the time domain, are nonlocal in time. In this work we study the validity of a singular limit (local in time) approximation for these nonlocal in time equations, by estimating the size of the difference of the fields as predicted by both models. In particular, we establish an a priori estimate for this difference, depending on the time horizon, properties of the domain, spatial properties of the initial data and the source terms and the chirality measure β of the approximating model.     

A note on the approximation of Dirichlet boundary control problems for the wave equation on curved domains

We consider an exact boundary control problem for the wave equation with given initial and terminal data and Dirichlet boundary control. The aim is to steer the state of the system that is defined on a given domain to a position of rest in finite time. The optimal control that is obtained as the solution of the problem depends on the data that define the problem, in particular on the domain. Often for the numerical solution of the control problem, this given domain is replaced by a polygon. This is the motivation to study the convergence of the optimal controls for the polygon to the optimal controls for the given domain. To study the convergence, the values of the optimal controls that are defined on the boundaries of the approximating polygons are mapped in the normal directions of the polygon to control functions defined on the boundary of the original domain. This map has already been used by Bramble and King, Deckelnick, Guenther and Hinze and by Casas and Sokolowski. Using this map, we can show the strong convergence of the transformed controls as the polygons approach the given domain. An essential tool to obtain the convergence is a regularization term in the objective functions to increase the regularity of the state.     

空间一维结构分布动载荷时域识别方法

提出一种适用于空间一维结构分布动载荷的时域识别方法.基于空间分段和时间分段的思想, 推导了载荷时程识别的公式和过程.用MATLAB编写了载荷识别程序,以受分布动载荷简支梁和受随机风载荷输电导线的载荷识别对方法和程序进行验证, 并通过仿真试验研究了噪声对载荷识别的影响.结果表明,该方法对于线性问题有很高的识别精度,对于弱非线性问题能够满足工程应用要求,为分布动载荷时域识别提供了有效的途径.