扩散方程源项识别反问题的正则化方法  

Regularization method for inverse problem of source term identification of diffusion equations

作　　者：郑江澎 冯立新[3] ZHENG Jiangpeng;FENG Lixin(China-Russian Joint Graluate Sehool,Heilongiang University,Harbin 150080,China;Department of Meehanics and Mathematics,Novosibirsk State University,Novosibirsk 630090,Russia;School of Mathematical Science,Heilongjiang University,Harbin 150080,Chima)

机构地区：[1]黑龙江大学中俄联合研究生院,哈尔滨150080 [2]俄罗斯新西伯利亚国立大学力学与数学学院,新西伯利亚630090 [3]黑龙江大学数学科学学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2020年第5期535-543,共9页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11871198)。

摘　　要：探讨扩散方程有界区域只含空间变量的源项识别反问题,基于Tikhonov正则化法提出了迭代正则化法,给出了精确解和正则化解的误差估计,通过选取适当的迭代数,迭代正则化法的源项恢复效果优于Tikhonov正则化法。The inverse problem of source term identification for a bounded region has been discussed,where the source term depends only on spatial variables.Based on the Tikhonov regularization method,an iterative regularization method is proposed,and the error estimates between the exact solution and the regularization solution are given.By selecting the appropriate iteration number,the source recovery effect of the iterative regularization method is superior to that of the Tikhonov regularization method.

关 键 词：扩散方程 源项识别反问题 迭代正则化 误差估计 

分 类 号：O241.82[理学—计算数学]