On the low regularity of the Benney-Lin equation

We consider the low regularity of the Benney-Lin equation ut+uux+uxxx+β(uxx+uxxxx)+ηuxxxxx=0. We established the global well posedness for the initial value problem of Benney-Lin equation in the Sobolev spaces Hs(R) for 0?s>−2, improving the well-posedness result of Biagioni and Linares [H.A. Biaginoi, F. Linares, On the Benney-Lin and Kawahara equation, J. Math. Anal. Appl. 211 (1997) 131-152]. For s<−2 we also prove some ill-posedness issues.     

离散形式的声阻抗反演问题的稳定性分析

1．引言考虑一维声波方程组从脉冲响应州附ω（0.t）反演声阻抗ε（x）,是一个适定问题（[1],[2],[3]）．声阻抗ε（X）具有明确的物理意义,它大于民与之对应的脉冲响应自然也应具有某种特殊的性质,本文对此进行深入的分析．本文首先引入KennethP．Bube和RobertBurrdge关于离散形式的声阻抗反演问题的一些基本结果,分析其实物理系统的脉冲响应的特征,说明了真实物理系统的脉冲响应具有某种正定性,这种特征是本质性的,由真实物理系统的内部固有性质所决定．在实际计算中,作为观测数据给出的脉冲响应数据如果具有这种特征,则反…     

An inverse contact problem in the theory of elasticity

In this paper, we discuss an inverse problem in elasticity for determining a contact domain and stress on this domain. We show that this problem is an ill‐posed problem, and we establish the uniqueness and L²‐conditional stability estimation for the stress. Copyright © 1999 John Wiley & Sons, Ltd.     

波动方程反演问题的一种新的逼近方法

本文给出了一种求解波动方程反演问题的“多目标函数法”.这种方法简单、有效,并具有明确的物理意义.对于三维问题的程序化它有很强的优越性.     

波动方程的差分反演模型

为了反演波动方程的系数函数,利用差分离散及扰动假设,推导出一个适合迭代的数值模型．解决了以往方法中正反演模型数值精度不一致问题,以及由此带来的一系列问题．经数值模拟计算说明,该方法是可行的和有效的．     

Determining the parameters of a stratified piecewise constant medium for the unknown shape of an impulse source

For a hyperbolic wave equation with some parameter λ, we consider the problem of finding the piecewise constant wave propagation speed and a series of parameters in the conjugation condition. Moreover, the shape is assumed unknown of the impulse point source that excites the oscillation process. We prove that, under certain assumptions on the structure of the medium, its sought parameters are determined uniquely from the displacements of points of the boundary given for two different values of λ. We give an algorithm for solving the problem.     

CLASSICAL SOLUTION OF QUASI-STATIONARY STEFAN PROBLEM

This paper considers the quasi-stationary Stefan problem:△u(x,t)=0 in space-time domain,u=0 and Vv (?)u/(?)u=0 on the free boundary.Under the natural conditions the existence of classical solution locally in time is proved bymaking use of the property of Frechet derivative operator and fixed point theorem. For thesake of simplicity only the one-phase problem is dealt with. In fact two-phase problem can bedealt with in a similar way with more complicated calculation.     

On the problem of determining the structure of a layered medium and the shape of an impulse source

For the equation of wave propagation in the half-space ? ₊ ² + = {(x, y) ∈ ?² | y > 0} we consider the problem of determining the speed of wave propagation that depends only on the variable y and the shape of a point impulse source on the boundary of the half-space. We show that, under some assumptions on the shape of the source and the structure of the medium, both unknown functions of one variable are uniquely determined by the displacements of boundary points of the medium. We estimate stability of a solution to the problem.     

半线性波方程的一个反问题

利用压缩映像原理讨论了一类半线性波方程确定未知系数的反问题,文中给出了该问题解的存在性、唯一性和稳定性。