一个抛物型方程逆问题的Fourier和小波正则化方法  

Fourier and Wavelet Regularization for an Inverse Problem of Parabolic Equation

作　　者：王义龙[1] 贺永春[2] 杨君慧 

机构地区：[1]西安电子科技大学理学院,陕西西安710071 [2]榆林学院数学系,陕西榆林719000 [3]陕西医学高等专科学校,陕西西安710068

出　　处：《榆林学院学报》2006年第2期1-4,共4页Journal of Yulin University

摘　　要：考虑非标准的一维逆热传导方程的定解问题。问题是不适定性的,即g(t)微小扰动会引起解的很大误差。通过Fourier方法,舍去g(t)的高频成分来正则化问题并给出了误差估计;利用M eyer小波在频域中的紧支撑性滤除g(t)的高频成分并结合G alerk in方法建立了正则化方法,给出了误差估计;对上述两种方法给出了数值实验并进行了比较和讨论。The sideways parabolic equation in the quarter plane is considered. This is an ill-posed problem： a small perturbation in the data g（t） may cause dramatically large errors in the solution. , We regularize the problem by eliminating high-frequency components and give the error estimate . We use Meyer wavelet whose Fourier transform has compact support to filter away high-frequency components of g（t）. Regularization is realized by using a Wavelet-Galerkin approximation. The error estimates and numerical experiments are given . The comparisons and discussions between them are also given.

关 键 词：逆问题 不适定问题 抛物型方程 小波Fourier方法 正则化 

分 类 号：O175[理学—数学]