Fourier正则化同时反演热传导方程的初值和源项  

The Fourier regularization simultaneously reverses the initial value and the source term of the heat conduction equation

作　　者：张建萍 熊向团 ZHANG Jianping;XIONG Xiangtuan(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《湖北大学学报（自然科学版）》2024年第4期565-573,共9页Journal of Hubei University：Natural Science

基　　金：国家自然科学基金(11661072);西北师范大学科学计算创新团队资助项目(NWNU-LKQN-17-5)资助。

摘　　要：研究边值问题中从已知的给定数据中同时识别初始条件和未知源的问题。用Fourier变换求出问题的精确解,发现该反问题是严重不适定的。为了解决所提出的问题,本文中用Fourier正则化方法构造出正则化解近似解,并在边界条件的假设下,得到先验参数选取下的精确解与其正则化近似解之间的对数型误差估计。We discussed the problem of identifying both initial conditions and unknown sources from a given data in the boundary value problem.The exact solution of the problem was solved by using the Fourier transform,and it is found that the inverse problem is seriously unstable.In order to solve the proposed problem,we used the Fourier regularization method to construct a regular solution approximation solution,and under the assumption of boundary conditions,the logarithmicerror estimate between the exact solution selected by the prior parameters and its regularized approximation solution was obtained.

关 键 词：热传导方程 不适定问题 Fourier正则化 同时反演 误差估计 

分 类 号：O241.8[理学—计算数学]