一类双曲型一维波动方程反问题解的整体唯一性

本文给出了一类双曲型一维波动方程反问题的解的整体唯一性定理。     

一类双曲型方程反问题的存在性与唯一性

针对双曲型方程定解问题{utt=a2uxx+f(t),0xπ,a∈R且a≠0,u(0,t)=v1(t),u(π,t)=v2(t),t0,u(x,0)=g(x),ut(x,0)=h(x),0≤x≤π研究了可以唯一决定未知函数组{v1(t),v2(t),f(t)}的基本条件,提出了该定解问题的反问题,并且讨论了此反问题的存在性与唯一性.     

代数特征值反问题可解的充分条件

本文讨论如下代数特征值反问题的可解性:问题G.设A=(a_(ij))和A_k=(a_(ij)~((k)))(k=1,…,n)是一组n+1个n×n实矩     

关于代数特征值反问题对称情况可解的充分条件

§1.引言 本文讨论下述特征值反问题的可解性: 问题 G.设A_0=(a_(ij)~((0)))和A_k=(a_(ij)~((k)))(k=1,…,n)是一组n+1个n×n实对称矩阵,λ_1,…,λ_n是n个不同的实数.求实数c_1,…,c_n使得矩阵A_0+sum from k-1 to n C_k·A_k的特征值为λ_1,…,λ_n. [1]和[2]曾给出此问题可解的充分条件.本文应用Rothe不动点定理[3]给出问题G可解的另外两个充分条件.本文的结果可判定[1]和[2]中定理所不能判定的某些问题     

线性方程组的反问题

给定线性方程组AX=b,易求其通解,设为     

伴随矩阵的反问题

伴随矩阵的反问题王新哲（保定师范专科学校数学系０７１０５１）设Ａ＝（ａｉｊ）为一方阵，记Ａ＊＝（Ａｊｉ），其中Ａｊｉ为ａｊｉ在Ａ中的代数余子式，则称Ａ＊为Ａ的伴随矩阵．然而，当给定一方阵Ｂ时，却不一定有方阵人使得Ａ＊＝Ｂ．如：Ｂ＝因三阶方阵Ａ的伴随矩...     

热传导反问题中非线性热源的存在性

研究热传导方程在一类非局部时间的边界条件下线性热源的反演问题。文中应用Ｓｏｂｏｌｅｖ紧性方法证明了热源在Ｈｏｅｌｄｅｒ空间中的（关于时间的）局部存在性。     

椭圆型方程的一个反问题

本文讨论了椭圆型方程发((?)~2u)/((?)y~2) (?)/((?)x)(a(x)((?)u)/((?)x))=0在区域x>0,y>0上确定未知系数a(x)的反问题,文中给出了局部解的存在性、唯一性。     

一类广义对称矩阵反问题有解的条件

本研究一奥广义对称矩阵反问题的有解条件．给出问题P有解的充要条件。     

解洞穴逆散射问题的一种正则化Newton方法

We consider the inverse problem to determine the shape of a open cavity embedded in the infinite ground plane from knowledge of the far-field pattern of the scattering of TM polarization.For its approximate solution we propose a regularized Newton iteration scheme.For a foundation of Newton type methods we establish the Fréchet differentiability of solution to the scattering problem with respect to the boundary of the cavity.Some numerical examples of the feasibility of the method are presented.     

A Regularized Newton Method in Inverse Scattering Problem from Cavities

We consider the inverse problem to determine the shape of a open cavity embedded in the infinite ground plane from knowledge of the far-field pattern of the scattering of TM polarization.For its approximate solution we propose a regularized Newton iteration scheme.For a foundation of Newton type methods we establish the Fréchet differentiability of solution to the scattering problem with respect to the boundary of the cavity.Some numerical examples of the feasibility of the method are presented.     

Uniqueness of the Solution to the Inverse Problem of Scattering Theory for the Sturm--Liouville Operator with a Spectral Parameter in the Boundary Condition

Mathematical Notes -     

A Method for Solving the Inverse Scattering Problem for Shape and Impedance of Crack

The inverse problem considered in this paper is to determine the shape and the impedance of crack from a knowledge of the time-harmonic incident field and the corresponding far field pattern of the scattered waves in two-dimension. The combined single- and double-layer potential is used to approach the scattered waves. As an important feature, this method does not require the solution of $u$ and $\partial u / \partial \nu$ at each iteration. An approximate method is presented and the convergence of this method is proven. Numerical examples are given to show that this method is both accurate and simple to use.     

Uniqueness Theorems for the Inverse Problem of Acoustic Scattering

Uniqueness theorems are obtained for the problem of determiningthe shape of a sound-soft or sound-hard obstacle from a knowledgeof (1) the far-field pattern at a fixed value of the wave numberand a finite number of distinct incident fields, or (2) thetotal scattering cross section for an interval of wave numbersand the incident field propagating in an arbitrary direction.     

Uniqueness in potential scattering with reduced data

We consider inverse potential scattering problems where the source of the incident waves is located on a smooth closed surface outside of the inhomogeneity of the media. The scattered waves are measured on the same surface at a fixed value of the energy. We show that these data determine the bounded potential uniquely.     

Uniqueness of two phaseless non-overdetermined inverse acoustics problems in 3-d

Uniqueness is proven for two non-overdetermined 3-d inverse problems of the determination of the spatially distributed sound speed in the frequency dependent acoustic PDE. The main new point is the assumption that only the modulus of the scattered complex valued wave field is measured on a certain set. The phase is unknown.     

An Example of the Absence of a Global Solution to Some Inverse Problem for a Hyperbolic Equation

We give an example of an inverse problem for a hyperbolic equation which has a unique local solution but no global solutions.     

An Improved Hybrid Method for Inverse Obstacle Scattering Problems

An improved hybrid method is introduced in this paper as a numerical method to reconstruct the scatterer by far-field pattern for just one incident direction with unknown physical properties of the scatterer. The improved hybrid method inherits the idea of the hybrid method by Kress and Serranho which is a combination of Newton and decomposition method, and it improves the hybrid method by introducing a general boundary condition. The numerical experiments show the feasibility of this method.