一类加权Kirchhoff方程正稳定解的非存在性

本文深入研究一类加权Kirchhoff方程■正稳定解的非存在性。结合试验函数法、截断技巧和反证法,在加权Sobolev空间中加权函数■和■满足适当条件下,建立了方程正稳定解的非存在性定理并给出了相应推论。     

关于矩阵方程A~TX+X~TA=B的极小范数解

作者讨论矩阵方程 ATX+ XTA=B。该方程在 Hamilton力学研究中有用。首先利用L yapunov方程证明了极小 Frobenius范数解的存在性和惟一性。然后用奇异值分解给出了求解最小范数解的一种方法。最后讨论极小范数解的向前扰动分析和最佳向后扰动分析     

带Sobolev临界指数的非齐次拟线性椭圆型方程正解的存在性

在RN上讨论带临界项的拟线性椭圆型方程正解的存在性问题。在一个正锥上应用Ekeland变分原理构造一个比P.S(.)c序列要弱的序列,通过证明该序列具有相对紧性,得到一个弱正上解,进而利用上下解方法得出所研究的问题至少存在一个弱正解。     

二阶微分方程解的渐近性的讨论

考虑如下的二阶方程 其中X(t,x,)是定义在域H:{0≤t< ∞,-∞0,n>0,f(t)为连续函数,f(t)≠0下讨论了方程(X)的不同类型解的渐近性态,给出了各种渐近解存在的充分必要条件。     

五阶斯托克斯波的简化解法及改进解

由于Ｓｋｊｅｌｂｒｅｉａ导出的确定五阶斯托克斯波的二个方程不易求解，本文将其简化为确定ｄ／Ｌ的一个方程：ｆ（Ｈ，Ｔ，ｄ，ｄ／Ｌ）＝０。根据这一简化解法，发现Ｓｋｊｅｌｂｒｅｉａ方程组的解有３种情况；存在唯一的精确解精确解不止一个；不存在精确解（但存在满足Ｓｋｊｅｌｂｒｅｉａ方程组方面的最佳近似解）。当精确解不止一个时，可应用变分原理的方法差别出合理的解，应用变分原理的方法还可将Ｓｋｊｅｉｌｂｒｉａ     

二阶微分方程解的渐近性的讨论

(一)引言 考虑如下的二阶方程 X=X（t,x,x）其中X（t,x,x）是定义在域H：{0≤t＜ ∞,-∞＜x∞＜ ∞,-∞＜x＜ ∞}上的连续函数，且满足解的存在唯一性条件和对初值的连续依赖性条件，x(t，x,x)是关于x的不减函数。     

一类广义Sine-Gordon方程的概周期解

用最大值原理和Banach压缩映像原理研究一类广义Sine-Gordon方程的概周期解问题,证明概周期解的存在‖u‖L∞<π2中的唯一性。     

具梯度项的次线性椭圆型方程解的分析

本文研究了1类具梯度项的次线性椭圆型方程大解和完全有界解的存在性问题。运用上下解方法和极值原理分别得到了Rn上方程存在完全大解的充分必要条件和存在完全有界解的充分条件,并且证明了该方程在Rn中光滑有界区域Ω上不存在大解。     

具梯度项的次线性椭圆型方程解的分析

本文研究了1类具梯度项的次线性椭圆型方程大解和完全有界解的存在性问题.运用上下解方法和极值原理分别得到了Rn上方程存在完全大解的充分必要条件和存在完全有界解的充分条件,并且证明了该方程在Rn中光滑有界区域Ω上不存在大解.     

二阶非线性抛物型方程的周期黏性解

将Hamilton-Jacobi方程黏性解的比较定理推广到二阶抛物型方程中,并结合Perron方法证明了二阶非线性抛物型方程的周期黏性解的存在唯一性。     

Moving shoreline boundary condition for nearshore models

The paper develops and analyzes two fully nonlinear boundary conditions that incorporate the motion of the shoreline in nonlinear time domain nearshore models. A moving shoreline essentially means the computational domain is changing with the solution of the flow. The problem is solved in two steps. The first is to establish an equation that determines the motion of the shoreline based on the local momentum balance. The second is to develop and implement into a shoreline model the capability of accommodating a changing computational domain. The two models represent two different ways of addressing this step: one is to track the position of the shoreline in a fixed grid by establishing a special shoreline point which generally is not a fixed grid point. The second is by a coordinate transformation that maps the changing domain onto a fixed domain and solves the basic equations in the mapped domain. The two shoreline conditions are tested against three known solution for nonlinear shoreline motion. Two are the 1-D solutions to the nonlinear shallow water (NSW) equations by Carrier and Greenspan [J. Fluid Mech. 4 (1958) 97], one representing the response to a transient change in the offshore water level, the other the motion due to a periodic standing wave, both on slopes steep enough to allow full reflection. The third is the 2-D horizontal (2DH) computational solution by Zelt [Coast. Eng. 15 (1991) 205] for the run-up of a solitary wave on a cusped beach. In all cases, both models are shown to behave well and give high accuracy results for suitably chosen grid and time spacings.     

Nonlinear wave profiles of wave–wave interaction in a finite water depth by fixed point approach

In this paper, a superposition of two periodic wave profiles in a finite water depth was investigated. This paper is focused on the improvement of a wave profile on the linear superposition of two waves. This improvement was realized by introducing an iterative method, which was based on a fixed point approach. Application of the fixed point approach to the wave superposition made it possible to obtain a wave profile of wave–wave interaction. The improved result of the wave profile was in good agreement with that of the nonlinear perturbation solution of the second order. It was interesting that the improved result revealed the higher-order nonlinear frequencies for two interacting Stokes waves while Dalzell's solution by a perturbation method could not predict them.     

Nonlinear response of membranes to ocean waves using boundary and finite elements

The behavior of a highly deformable membrane to ocean waves was studied by coupling a nonlinear boundary element model of the fluid domain to a nonlinear finite element model of the membrane. The hydrodynamic loadings induced by water waves are computed assuming large body hydrodynamics and ideal fluid flow and then solving the transient diffraction/radiation problem. Either linear waves or finite amplitude waves can be assumed in the model and thus the nonlinear kinematic and dynamic free surface boundary conditions are solved iteratively. The nonlinear nature of the boundary condition requires a time domain solution. To implicitly include time in the governing field equation, Volterra's method was used. The approach is the same as the typical boundary element method for a fluid domain where the governing field equation is the starting point. The difference is that in Volterra's method the time derivative of the governing field equation becomes the starting point.The boundary element model was then coupled through an iterative process to a finite element model of membrane structures. The coupled model predicts the nonlinear interaction of nonlinear water waves with highly deformable bodies. To verify the coupled model a large scale test was conducted in the OH Hinsdale wave Research Laboratory at Oregon State University on a 3-ft-diameter fabric cylinder submerged in the wave tank. The model data verified the numerical prediction of the structure displacements and of the changes in the wave field.The boundary element model is an ideal modeling technique for modeling the fluid domain when the governing field equations is the Laplace equation. In this case the nonlinear boundary element model was coupled with a finite element model of membrane structures, but the model could have been coupled with other finite element models of more rigid structures, such as a pontoon floating breakwater.     

海洋石油管道单点提升分析

基于管道微单元体平衡建立了海管单点提升的非线性力学模型的控制微分方程组 ,使用变弧长的无量纲代换将动边界问题化为固定边界的两点边值问题 ,利用Maple环境下编制的两点边值问题的打靶法程序得到了该问题在各个提升阶段的数值解答和在单点提升过程中管道的极限弯矩约为 0 .71q1 3(EI) 2 3。     

带梯度项的半线性椭圆型方程正径向整大解的存在性

本文研究带梯度项的半线性椭圆型方程正径向整大解的存在性.先利用Banach不动点定理和反证法得出正径向解的局部及整体存在性,进而得到正径向整大解的存在性结论.结果发现,正径向整大解的存在性依赖于梯度项的系数符号和指数的范围.     

A new kind of nonlinear mild-slope equation for combined refraction-diffraction of multifrequency waves

This paper presents the numerical solution of a new nonlinear mild-slope equation governing waves with different frequency components propagating in a region of varying water depth. There are two new nonlinear equations. The linear part of the equations is the mild-slope equation, and one of the models has the same non-linearity as the Boussinesq equations. The new equations are directly applicable to the problems of nonlinear wave-wave interactions over variable depth. The equations are first simplified with the parabolic approximation, and then solved numerically with a finite difference method. The Crank-Nicolson method is used to discretize the models. The numerical models are applied to a set of published experimental cases, which are nonlinear combined refraction-diffraction with generation of higher harmonic waves. Comparison of the results shows that the present models generally predict the measurements better than other nonlinear numerical models which have been applied to the data set.     

A Time-Domain Coupled Model for Nonlinear Wave Forces on A Fixed Box-Shaped Ship in A Harbor

A 2-D time-domain numerical coupled model is developed to obtain an efficient method for nonlinear wave forces on a fixed box-shaped ship in a harbor.The domain is divided into an inner domain and an outer domain.The inner domain is the area beneath the ship and the flow is described by the simplified Euler equations.The other area is the outer domain and the flow is defined by the higher-order Boussinesq equations in order to consider the nonlinearity of the wave motions.Along the interface boundaries between the inner domain and the outer domain,the volume flux is assumed to be continuous and the wave pressures are equal.Relevant physical experiment is conducted to validate the present model.It is shown that the numerical results agree with the experimental data.Compared with the coupled model with the flow in the inner domain governed by the Laplace equation,the present coupled model is more efficient and its solution procedure is more simple,which is particularly useful for the study on the effect of the nonlinear wave forces on a fixed box-shaped ship in a large harbor.     

完全非线性波浪与二维固定结构物作用的IGN-BEM耦合分析模型

为高效准确地对完全非线性波浪与二维固定结构物的相互作用进行模拟分析,建立了二维完全非线性时域耦合模型。耦合模型将计算域划分为靠近结构物的内域和远离结构物的外域,每个区域均采用满足完全非线性自由水面边界条件的波浪模型进行求解。在内域使用Laplace方程描述流体运动并采用高阶边界元法（BEM）对其进行求解;而在没有结构物的外域,波浪运动的控制方程为Irrotational Green-Naghdi（IGN）方程并采用有限元法（FEM）对其进行求解。内域和外域通过一段重叠区域进行耦合,从而实现模型间变量的传递。首先利用耦合模型分别对规则波的传播、直墙前立波的生成以及相关物理模型试验进行模拟,数值结果与精确解和试验结果的良好吻合验证了耦合模型耦合方式的合理性以及处理非线性问题的准确性;然后使用耦合模型模拟分析了波浪与固定结构物间的相互作用,并将结果与线性解析解以及完全非线性BEM模型的结果进行了对比分析,进一步证明了耦合模型的正确性与高效性。     

海雾形成机制的初步研究

海雾是近海面层大气的水汽凝结现象.这种现象的发生是大气与海洋及大气内部热量和水汽交换的结果.Rodhe,B.[1]曾用湍流扩散方程讨论过湍流对雾形成的作用.Fisher,E.F.和Caplan[1]首次对雾和层云的形成进行数值试验.     

NONLINEAR INTERACTIONS AMONG GRAVITY SURFACE WAVES

Based on the perturbation method, a fourth order theory for nonlinear interactions among three dimensional gravity waves in water of any uniform depth is presented in this paper. Two cases are considered: ( i ) wave number vectors fixed, frequencies perturbed, and ( ii ) wave number vectors and frequencies both fixed. According to this solution, expressions of thesame order for progressive waves, short-crested waves and nonlinear interaction between wave and vertical wall are also derived'