抛物方程热源识别的中心差分正则化方法  

Central difference regularization method for identifying heat source in parabolic equation

作　　者：杨帆[1] 郭亨贞[2] 万诗敏[3] 李晓晓[1] 

机构地区：[1]兰州理工大学理学院,甘肃兰州730050 [2]兰州城市学院教育学院,甘肃兰州730070 [3]天津城市建设学院基础学科部,天津300384

出　　处：《兰州理工大学学报》2011年第6期140-144,共5页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(10671085)

摘　　要：探讨一类抛物方程只含有空间变量的热源识别反问题.这类问题是不适定的,即问题的解不连续依赖于测量数据.利用中心差分正则化方法,得到问题的一个正则近似解,并且给出正则解和精确解之间具有HO¨lder型的误差估计.数值实验表明中心差分正则化方法对于这种热源识别是非常有效的.The inverse problem of heat source identification of a class of parabolic equations with spatial variable alone was discussed. This problem was ill-posed, i.e. the solution does not depend continuously on the data measured. A regularization approximate solution of the inverse problem was obtained by using central difference regularization method and it was given that there was HOlder type stability estimate between the regularization solution and exact solution. Several numerical examples showed that the central difference regularization method would work effectively for identifying the heat source.

关 键 词：热源 正则化 抛物方程 中心差分 

分 类 号：O175.26[理学—数学]