{"title":"An Iterative Regularization Method for Solving Backward Problems With 2 Perturbation Data","authors":"YUAN Xiaoyu, FENG Xiaoli, ZHANG Yun","doi":"10.21656/1000-0887.440066","DOIUrl":null,"url":null,"abstract":"The backward problem of space-fractional diffusion equations with perturbed diffusion coefficients and perturbed final data was considered. The initial data were recovered from the measured data at the final time. Given the severe ill-posedness of this problem, an iterative regularization method was proposed to tackle it. The convergence error estimate between the exact and approximate solutions was obtained under the assumption of an a-priori bound on the exact solution. Finally, several numerical simulations were conducted to verify the effectiveness of this method.","PeriodicalId":8341,"journal":{"name":"应用数学和力学","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"应用数学和力学","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21656/1000-0887.440066","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
The backward problem of space-fractional diffusion equations with perturbed diffusion coefficients and perturbed final data was considered. The initial data were recovered from the measured data at the final time. Given the severe ill-posedness of this problem, an iterative regularization method was proposed to tackle it. The convergence error estimate between the exact and approximate solutions was obtained under the assumption of an a-priori bound on the exact solution. Finally, several numerical simulations were conducted to verify the effectiveness of this method.
期刊介绍:
Applied Mathematics and Mechanics was founded in 1980 by CHIEN Wei-zang, a celebrated Chinese scientist in mechanics and mathematics. The current editor in chief is Professor LU Tianjian from Nanjing University of Aeronautics and Astronautics. The Journal was a quarterly in the beginning, a bimonthly the next year, and then a monthly ever since 1985. It carries original research papers on mechanics, mathematical methods in mechanics and interdisciplinary mechanics based on artificial intelligence mathematics. It also strengthens attention to mechanical issues in interdisciplinary fields such as mechanics and information networks, system control, life sciences, ecological sciences, new energy, and new materials, making due contributions to promoting the development of new productive forces.