二维波动方程系数反问题的一种求解方法

A Solving Method of Inverse Problem by Determining Coefficient for Two-dimensional Wave-Equation

讨论了无界域上二维波动方程U_(11)-K^2(x,y)(U_(xx)+U_(yy))=O关于x离散得到相应的离散问题,它是一维情形的方程组。在假定系数K(x,y)关于x化较小的情形下,把它化为第二类积分方程组,构造了求解离散问题的迭代方法,这种迭代在局部范围内收敛,并证明了离散问题存在唯一解。

This paper discusses the scatter problem about χ for two—dimensional wave equation U,,—K^2(x,y) (U_(xx)+U(yy))=0 in no limit rang. It is an equation group for one—dimension, Under the assuming condition of the coefficient which changes smaller about χ, we turn the problem into integral equations of second type. Then we structure interational method for solving scattering problem. The main results are that we prove the convergence of this method in part range and consequently the existence and unicueness of the scattering problem.